There are many shelf-stable probiotics on the market that can offer you the benefits of probiotics without having to worry about keeping them in a cold environment.
Probiotic formulas can be naturally shelf-stable based on the species/strain, or through processing. These probiotics come from some of the leading companies and are shelf-stable without the need for refrigeration.
Probiotics that are naturally shelf-stable include but are not limited to spore-based probiotics and Saccharomyces boulardii, a probiotic yeast. Spore-based formulas feature Bacillus species from the soil. These soil-based probiotics are naturally stable due to the formation of a hardy spore.
Other probiotics may not be shelf-stable, but their mechanisms not require the organism to be "living" to offer benefits.
Known as "ghost probiotics", this is an up-and-coming understanding of probiotic mechanisms and your choice of probiotic can differ based on your goals. The best example is PyloGuard, a unique strain that binds H. pylori cells and carries them out of the stomach where they are later eliminated in the stool. The binding of unwanted H. pylori overgrowth does not require the organism to be living!
Others may not have a true colonizing effect but help modulate or stimulate the body in a specific way due to the body's response to it while transiting in the gut. The best example is Zenbiome Cope and Zenbiome Sleep by Microbiome Labs for psychological benefit for stress balance and mood support.
Another important factor is that a probiotic may be shelf-stable, but if not protected from stomach acid, it could be a waste as many Lactobacilli/Bifidobacteria are vulnerable to the acidic pH whether stable on a shelf or not.
Look for Stomach Acid Protection
Probiotics that contain technology to protect organisms from the stomach acid are MORE important than shelf-stability alone. Ideally, you need both unless you're looking for the transient modulating/stimulating/binding effects of a specific strain.