Would the problem be corrected if a simple Heat/Cold manual thermostat was installed?
Usually it is the thermostat or a intermitent short in the thermostat wiring that is the problem. Now if it is just the air move/blower fan that is causing the problem an adjustment to the fan and limit control or fan control itself could be the problem. It could also be the adjustment for heat anticipation in the thermostat if so equiped.