On Thursday, December 7, 2017 at 10:41:33 AM UTC-5, condo owner wrote:
On my TOTALINE P474-1035 thermostat, I've set the desired temperature at 82° but the furnace stops when the room temperature reaches 76°.

A "Heat/Cool Indicator" light is located between the temperature UP & DOWN buttons. According to the owner's manual, this "Bi-color LED" light "will only energize if the thermostat is system powered". This light stays on (red) even after the furnace stops when the room temperature reaches 76°. My guess is that the light would go out if the room temperature would reach 82°.

Assuming that led behaves that way when the thermostat is set to lower temps, ie it's on when the furnace is on, out when it shuts off, then I'd say your guess is correct. This could be what I said earlier, it may have a fail-safe mechanical temp switch that opens if the temp is abnormally high. It may be defective, opening too low, at 76,in which case the light stays on, but the circuit to the furnace is open, ie no call for heat. I'd say time for a new thermostat.