The short answer to the above questions is yes and no. Or at least, not necessarily. We'll have to unpack that a little. Raw foodies and paleo folks, hold on to your panties on this one, it might just blow your mind.
I'll explain a little more about what probiotics and their benefits are below, but the primary focus of today's article has to do with heating probiotics, and whether or not that a) kills the beneficial probiotics and b) if heat kills the probiotics, whether or not they're still beneficial.
The full answer might surprise you :) And those who also dislike cold sauerkraut can rejoice, there is hope for hot bacteria yet...
So bear with me for a minute or two ladies and gents, we're about to do a teeny tiny bit of two things I like to call logic and science.
The reason this is a two part article is because I don't always like cold sauerkraut or kimchi or miso. I'm also allergic to a lot of raw foods, and heating can sometimes destroy the allergen protein that causes an allergic reaction. Raw carrots and me don't always agree, but raw carrots - shredded in hot kimchi - and I get along just fine.
Furthermore, many probiotics food items - unless you make them yourself - come packaged, which often means they've been heated in order to seal the package.
Doing a little internet search pulled up a ton of websites that said YES! Heat kills probiotics and therefore you MUST eat it raw and not heated.
I wasn't convinced, however, that just because something is dead (in this case, those healthy little microorganisms) means that it also disappears. So if probiotics are dead, but not gone, can they not still do some good?
What are Probiotics?
By now many of you have probably already heard of probiotics, those healthy little microorganisms that are good for your gut and can be found in fermented foods like yogurt, sauerkraut, kimchi, miso, kombucha, and more. When we talk about probiotics in general we're talking about strains of Lactobacillus and Bifdobacterium.
Technically put, probiotics are classified by the World Health Organization (WHO) and the Food and Agriculture Organization of the United Nations (FAO) as:
"live microorganisms which when administered in adequate amounts confer a healthy benefit on the host" 
Where can you find probiotics?
Probiotics can be found in a variety of fermented foods and supplements, such as (and yes, I have some recipes linked below):
What are the health benefits of probiotics?
I get into the allergy aspect A LOT in my book Living with Oral Allergy Syndrome: A Gluten and Meat-Free Cookbook for Wheat, Soy, Nut, Fresh Fruit and Vegetable Allergies , but since this is an allergy blog, I thought I'd share another recent study in which researchers reviewed a variety of studies pertaining to allergies and probiotics and found that the majority of studies (17 of 23) "showed that people with seasonal allergies who took probiotic supplements or ate foods containing probiotics showed improvement in at least one outcome measure, such as improving their allergy symptoms, or their general quality of life, compared with allergy sufferers who took a placebo..." 
Does Heat Kill Probiotics?
Ok, so here's the first big question, right? Because if you throw some sauerkraut into your borscht, as I like to do in this Vegan Borscht recipe, or you want to toss some kimchi with your scrambled eggs in the morning, you want to know if you're killing all the good stuff, right?
The answer is probably yes. Probably. Because I haven't been able to determine at what heat different strains of probiotics are killed off. As far as I can tell, no scientist has put together a chart listing at what temperatures the various strains die.
So if you warm your kimchi in a pan, or bake your yogurt in a muffin, it may or may not die. This likely depends on the temperature, the item of food, and the particular strain of probiotics involved.
But here's the sticky point. A lot of websites out there will argue that, if it does die with the heat, it's no longer a probiotic, because the very definition of probiotic (as mentioned above) is a live microorganism.
However, as I said before, just because a bacteria (probiotic) is no longer alive doesn't necessarily mean it disappears along with its health benefits.
Here comes the good part...
It's called science.
Well, okay, about as much science as a non-science person with no legal liability or medical training can provide. This is in no way medical advice, by the way, as I'm not a medical professional. See your doctor for questions! : )
Can heat-killed / dead probiotics still have health benefits?
( Get out your happy horns and party hats, cold sauerkraut-haters, you're gonna like this one.)
The answer, according to numerous studies, seems to be YES!! YES!! And sometimes, even heat-killed probiotics produced similar results to live probiotics. (Heat-killed being probiotics that have been killed by heating.)
I give you the science to prove that there is a good likelihood that heating probiotics, while killing them, does not necessarily destroy their healthy properties (in some cases, it may alter it for a different beneficial effect, or lessen it to some extent, but doesn't necessarily do away with it all together)
* A study from 2009 in Pediatric Research found that the both the live AND heat-killed probiotic strain Lactobacillu rhamnosis GG (LGG) ameloriated intestinal and other organ inflammation in infant rats
* In 2010 researchers found that "many of the effects obtained from viable cells of probiotics are also obtained from populations of dead cells." Dead probiotics, such as bifidobacteria and
Enterococcus faecalis were found in different cases to stimulate the gastrointestinal immune system in chicks, and were beneficial to even healthy dogs. The article suggests that while live probiotic cells can be beneficial to gastrointestinal microflora, while dead ones could exert an anti-inflammatory response. 
* Another study found heat-killed Lactobacillus acidophilus effective at inhibiting bacterial Salmonella invasion of mouse organs  while another found that "lactobacilli can induce some (limited) protection (pro-biotic effect) against candidiasis in mice." 
* A study on elderly people found that those who took heat-killed Lactobacillus rhamnosuswere significantly less likely to suffer from the common cold than those that took a placebo.
So there you have it!! Just because something is dead doesn't necessarily mean it's gone.
This isn't to say there doesn't need to be more research done, and it seems that the benefits of heat-killed vs live probiotics might be different in certain cases. So it might not hurt to have some raw stuff AND some dead stuff from time to time.
But just like in my article on The Health Benefits of Raw vs Cooked Vegetables, sometimes science defies conventional logic (and raw foodies ;p ) and helps those of us who can't always have raw food.
What are some of your favourite probiotic foods?
Do you incorporate them into other recipes?
Looking for more research like this? Check out my book Living with Oral Allergy Syndrome: A Gluten and Meat-Free Cookbook Wheat, Soy, Nut, Fresh Fruit and Vegetable Allergies or Order from Amazon.com here!
 pg 9 of this massive report on probiotics from FAO/WHO ftp://ftp.fao.org/docrep/fao/009/a0512e/a0512e00.pdf
 Kechagia, Maria, Dimitrios Basoulis, Stavroula Konstantopoulou, Dimitra Dimitriadi, Konstantina Gyftopoulou, Nikoletta Skarmoutsou, and Eleni Maria Fakiri. "Health benefits of probiotics: a review." ISRN nutrition 2013 (2013).
 Li, Nan, W. Michael Russell, Martha Douglas-Escobar, Nick Hauser, Mariela Lopez, and Josef Neu. "Live and heat-killed Lactobacillus rhamnosus GG: effects on proinflammatory and anti-inflammatory cytokines/chemokines in gastrostomy-fed infant rats." Pediatric Research 66, no. 2 (2009): 203-207.
 Abstract for: Adams, Clifford A. "The probiotic paradox: live and dead cells are biological response modifiers." Nutrition research reviews 23, no. 01 (2010): 37-46
 Lin, W‐H., B. Yu, C‐K. Lin, W‐Z. Hwang, and H‐Y. Tsen. "Immune effect of heat‐killed multistrain of Lactobacillus acidophilus against Salmonella typhimurium invasion to mice." Journal of applied microbiology 102, no. 1 (2007): 22-31.
 Wagner, R. Doug, Carey Pierson, Thomas Warner, Margaret Dohnalek, Milo Hilty, and Edward Balish. "Probiotic effects of feeding heat-killed Lactobacillus acidophilus and Lactobacillus casei to Candida albicans-colonized immunodeficient mice." Journal of Food Protection® 63, no. 5 (2000): 638-644.
 Shinkai, Shoji, Masamichi Toba, Takao Saito, Ikutaro Sato, Mina Tsubouchi, Kiyoto Taira, Keiji Kakumoto et al. "Immunoprotective effects of oral intake of heat-killed Lactobacillus pentosus strain b240 in elderly adults: a randomised, double-blind, placebo-controlled trial." British Journal of Nutrition 109, no. 10 (2013): 1856-1865.