Yes!
Thermometers are food-contact surfaces, which means they can easily spread pathogens if not cleaned properly. You should follow the same cleaning procedures for thermometers as with other utensils. It is a good idea to clean and sanitize your thermometers after every use, to keep them clean and ready to go. There are some exceptions, but if you’re using your thermometer to measure different foods, it’s a good idea to clean and sanitize it between uses.