Sorry, my brain is wired with Fahrenheit not Celsius, LOL! But, yes, 37.5C is perfect, actually.
As for handling eggs, you actually are more danger to the eggs than they are to you, as a human hand can carry thousands and thousands of bacteria and viruses (virii) that can possibly enter the eggshell and kill the fetus inside. You need to have very clean hands (scrub really good with soap and water, and maybe even use hand sanitizer) before you touch hatching eggs. One suggestion given above was to adapt egg cartons to hold the eggs and just move the carton where one end is up, then change it so the other end is up, 3 to 5 (or even 7) times a day (always an odd number, not even). Then when they are nearing hatching day, you need to take them out of the carton and lay them flat, make sure the incubator's water reservoir is full, and then keep the incubator shut until all the eggs have hatched or all the hatched babies are dry.