I have my thermostat set on a program. It comes on every day at 430 and temp is set at 62. This is heat by the way. Usually by 5 it is up to 62. The furnace will stay on until 11 and then turn off. If I go over to the thermostat and press the down button and set it at 60 then set it back to 62 it shuts off. Shouldn't it be shutting off during the program?

If it is a modulating furnace, it may be turning itself down to a very low firing rate to maintain the temperature. Does the temperature ever go above 62?