Why does my thermostat turn the heat on when set to a high temperature when it's cold and turns the heat on at a low temp setting when warm.?

Thermostat is bad.  Replace it.

It sounds like the thermostat mode is in the automatic position instead of the heat mode.  In automatic, the heat will come on when room temperature is lower than the setpoint.  The A/C comes on when room temperature is higher than setpoint. If you're simply listening for the vent fan running, the vent fans runs in both the heat mode and A/C mode.  You may confusing the A/C as a heater.  If you change the mode from automatic to heater, it may work as expected.  In heat, when the temperature setpoint is higher than room temperature, the heat will come on.  When the temperature setpoint is lower than room temperature, the unit should stay down.