They do make compost thermometers. Check any gardening catalog. It should run you about $14. Measuring the actual temp gives you an idea when the pile is done cooking. I posted a link to a compost journal that I did a couple of years ago, and the core temp drops gradually over time. One might think that they're doing something wrong, but it's just an indication that the compost is almost ready for use. Of course, it doesn't hurt to let it age for a while, but if you're hot composting, then you want the compost in 2-4 weeks.
Don't stick your hand directly into the middle of a hot compost pile. The temps can reach 150 degrees F the first week. You can easily get a burn that way.
Otherwise you can use the obvious: put your hand over a recently turned pile, and you feel the heat. Steam will rise off of the pile as you turn it. You can use an indirect method too: after you have turned your pile, carefully touch the metal part of whatever you used to turn the pile to see how hot it is. Again, be cautious of burns using this method.
