An HVAC system includes an HVAC unit having a cooling mode and a heating mode for conditioning the air in an inside space, and a programmable thermostat located remotely from the HVAC unit. The HVAC unit may have an onboard controller configured to control when the HVAC unit is in the cooling mode or heating mode, and whether the HVAC unit is activated or not. In some cases, the onboard controller of the HVAC unit may use a common temperature setpoint when controlling in the cooling mode and the heating mode. The programmable thermostat may have a programmable schedule with a plurality of time periods, where each time period has a heating setpoint and a cooling setpoint separated by a dead band. The onboard controller of the HVAC unit may be configured to accept input signals from the remotely located thermostat. The remotely located thermostat may send one or more input signals to the onboard controller of the HVAC unit in accordance with the programmable schedule, where the one or more input signals cause the onboard controller of the HVAC unit to set the HVAC unit to a particular one of the cooling mode and the heating mode, and to activate the HVAC unit so as to condition the air in the inside space in the particular one of the cooling mode and the heating mode.