1993 Toyota Corolla Intermittent Heat and fluctuations in t

Just got back from vacation and my car has been sitting for over a week in the driveway. While it likely got below freezing a few nights (we are in CT) the temperatures are still fall-like. When I started it Monday and turned on the heat it did not produce heat up for my entire 15 minute ride (13 miles) to work even though the gauge showed that it was at the midpoint (normal) for most of the ride. The next AM I started it and let it idle for almost 30 minutes. When I drove it to work it had great heat inside, but the thermostat began to fluctuate all over the place. To avoid overheating I put the heat on high and it seemed to control it as well as the speed I was traveling on the highway. The next day I had no heat in the AM on the way to work and then it eventually provided heat. Is this a thermostat issue or a problem with the radiator? I have replaced thermostats on older vehicles, but can I do the same with this vehicle? Thanks for any assistance that you can provide.