I just use an acurite digital thermometer. I don't know how long I've had it 5-6 yrs.
Yes, it does get pooped on, I clean it up by wiping it by a damp paper towel and lysol.
It's always a good idea to keep a watch on temperature, but chick behavior is a very good indicator of how hot/cool they are.
If they avoid heat=too hot
If they huddle under the heat=too cold.
You want chicks spread out fairly well. One warm spot in the brooder and let the rest be cool.
All that said, I abandoned using a heat lamp a few years back and now use a heating pad. Chicks do very well, they sleep through the night, less risk of fire, etc. I DO put the thermometer in their heating pad "cave" just to make sure it's warming, but the chicks will let you know if it's cold - they scream LOL I've found if you insulate the cave with either more towels or even with bedding (heaping on top) the temp can go way up, so you want to watch that (they won't go in their cave if it's too hot).
Good luck with your babies - we would love to see them - do you have photos?