Mites SUCK, as they WILL spread. so just do your self a favor. find a product thats designed to kill snake mites and that lasts to kill the hatching eggs. treat all your reptiles. and be done with it.
tepid water is basically around 85*F which will feel wet, not hot or cold to you. another word of advice is wash your cloths immediately, they can hitch hike. also if you have carpet. i like to spray mine with PAM around the base of my vivs to ensure any adventurous ones kick the bucket too. Mites can become a reoccurring battle fast and its not fun.