I have an older Honeywell thermostat that is exhibiting this problem.

I will set the thermostat to around 72*F.
The function switch is set to HEAT (not COOL or OFF)
The fan is set to AUTO

Even if the thermostat temperature reading is less than 72*F, the heater will not kick on. I have not tried in COOL yet.

If I desire to, I can put the fan on ON and the system will begin heating the house, but this of course will continue to run until I put the switch back to AUTO.

Sometimes I can switch the function from OFF to HEAT a few times and slide the temperature up to 80*F and the heater will kick on in AUTO mode.

Is the thermostat simply not calibrated? Or is this a furnace problem?