I use the same thermometer throughout the brew. It doesn't need to be sterilised between each stage.
As long as it's clean at the start, it'll be fine for using during the mash process, sparge etc without being sterilised. Any nasties that might be on it wouldn't survive when you get onto the boil stage and will be wiped out then.
This goes for any equipment you use before the boil, as long as everything is clean, it doesn't need to be sterilised at this stage.
As I put it into the boiler to measure the boil temp, it'll get sterilised at that point. So will then be sterile for the cooling temp measurements.
It's only after the boil that you need to pay attention that everything is sterilised.
You could if you wanted, just put some steriliser in a trial jar & put your thermometer back in that between each stage if you were worried. Just remember to rinse it off before using it. But this probably isn't necessary.
Fermenter heaters?