We had a lot of trouble with short cycling when we moved into our current house. It was more with the AC than with the heat. I tried different things, including a fancy new thermostat that had an adjustable range between the "on" and "off" temperatures. Nothing seemed to work. Then, one day I was fiddling with it and I just happened to have the thermostat pulled away from the wall. The AC came on, and I immediately felt a cool blast of air coming out of the hole in the wall for the thermostat wire. With the system running, a pressure differential existed between the basement and the upstairs, causing cool basement air to enter the stud cavity and exit through the thermostat wire hole in the wall. It caused premature cooling of the thermostat, which then shut the system off. I plugged the hole with a little caulk, and after that everything worked fine!
Again, we had more trouble with AC than with heat, but it's possible you could have a similar problem.
John