It all comes down to personal choice now doesn't it?
If I was running in the heat I'd keep my fanny pack on and run with my S&W 642 revolver. I'm not totally without hot weather experience. I lived in Texas for 3 years and southern Ohio for 3 years as well. The day I couldn't run with my 38 in a fanny pack is the day I'd give up running. Would I run with any sized gun in my pocket? No.
MY lower limit for personal defense is 38 sp or 9mm. A lot of people agree with me. So what. If you are happy with a smaller gun in a lower caliber than I then more power to you. Carry the 22. Just don't try to tell me carrying a slightly larger gun in hot, humid weather isn't doable or that it will break my stride.