I agree with the above. It sounds like a probe issue. Even when my temps in my room go up my thermostat keeps the temps proper. The only one I have issues with is my QT rack and that's because it's on a rheostat. I check the room a bunch throughout the day but the Herpstat never changes. I have an open rack design but I also have a heated room. An oil heater sounds like a bad idea during the summer. It takes a long time to heat and cool. You might try a small ceramic forced air heater for the warmer months. I use one all the time because they are efficient and can quickly change the temp one way or the other depending on how it is set. An oil heater is much more suited for keeping a steady temp in the colder months because the oil retains the heat.
Regards,
B