In our last midwestern home, we had a gas furnace. In the winter we'd set it at a temperature, it would come on and give heat, and then it would shut off and all was well. Now in South Dakota we have an electric furnace. We set the thermostat to 70 degrees. The furnace comes on and heats the house as norma,l but then the fan keeps on running and running and sends out so much cold air that the house gets cold and the cycle starts again. Is there a chance there's a heat pump involved?
Indeed, it sounds like you have an electric heat pump! Install a thermostat designed for a heat pump - they're different from those designed for gas furnaces, and manage the heat better when an electric heat pump is involved.