How warm is water in nature? I think clean and fresh is more important.
Misting is not really much like rain anyway, especially by hand. Some reptiles just hate it.
As for temperature of mist, I dont think they are quite as sensitive as people would beleive, its not like our skin.
1 they are ectotherms, we're not, cold or warm water on our skin is noticed (skin/nerve structure is different for us)
2 reptile skin is designed to keep moisture in.
3. consider how common thermal burns are in captive reptiles, if it can sit under/against heat long enough to burn, even cook to death and not notice, do you really think it will notice, care, or come to harm if your misting water is room temp/cold?
As long as you dont use ice-cold or refridgerated water (it will still cool it some) it will be fine. A nice warm shower is not something nature provides often.