Furnace won't adjust to thermostat setting
Does the furnace shut down when the thermostat stops calling for heat (or very soon after)?
Furnace
If the furnace does not shut down when the thermostat stops calling for heat, it's a problem with the furnace. It likely won't stop immediately, but should stop fairly soon after.
Thermostat
If the thermostat does not stop calling for heat once the set point is reached, it's a problem with the thermostat. Usually there is some form of indicator on the thermostat, that lets you know when it's calling for heat.
Read the manual for the thermostat, and make sure you're programming it properly.