Is it Normal if my Thermostat Makes a Clicking Noise?
It is normal for the thermostat to make clicking noises.
The clicking noises are the relay opening and closing to let the power through to the heating system. While it should be hardly noticeable, it can be reduced by insulating the surrounding of the electrical box in which it is mounted. You should also ensure that the screws mounting both the box and the thermostat are tight.