When making homemade yogurt, is it safe to put a metal thermometer in?

I am making 24 hour yogurt and want to know if the temperature is stabilized between 97-107 with a heating device I use. There is water at the base but this doesn't reflect the heat of the yogurt due to the heat bounced off the jar walls. So the best way would be to stick the thermometer in the yogurt after 10, 15, 20 hours while it's fermenting -- but does the metal kill the starter culture or mess with it?