If the HVAC system remains under warranty, calling a pro to check the thermostat is wise. However, if the warranty has expired, do-it-yourself homeowners with some electrical experience can repair thermostats themselves as long as they are familiar with necessary safety precautions.
If a furnace doesn't heat, for example, one option is to clean components under the thermostat cover. Thermostats that do not have a mercury switch can benefit from having the bimetallic coil and switch contact surfaces cleaned, which can make the furnace return to life. If the furnace keeps turning on and off, or "short cycling," the components in the thermostat could also be dirty. More significant repairs involving the thermostat, such as total replacement, may require the services of a licensed professional.