I have a honeywell 7 day programmable thermostat (20 yrs old) - the autofan mode stopped working. The heat works only when switched to 'on'. When it is sleep mode/on I have it set to 63, but it goes up to 72. We just replaced the blower motor because it burnt out. Do I need a new thermostat?

If the furnace is as old as your thermostat you may have a bad fan/limit control switch. They are made to bring on the blower after the heat exchanger is heated up. Over time they go weak and will not bring on the blower.