Bathing in Nix solution has caused death from drinking the water. The Nix treatment is so effective, that this bathing step is unnecessary anyway (you can do the soapy water soak if you want, but this won't stop the cycle). You can spray the nix solution on the animal. I only sprayed my snake once and with the rest of the treatment, was enough to erradicate them all within a very short period of time. I did not see any mites after the first treatment, but I believe I re-sprayed everything again at least every time the cage needed cleaning for a couple of weeks.
I believe higher temps will only speed up the mite life cycle.
Christina, I think mykee means spray with Nix solution 2x/week. If you have rack systems, you can also smear some petroleum jelly (vaseline) around the outsides of the ventilation holes to catch escapees.