I had the same issue with my heater and I returned it and the new one did the same thing. So now i just leave the heater unplugged since the water temp stays between 78 and 82 without it. I'm sure I'll have to plug it in during the colder months. I do leave my lights off during the hottest part of the day as well. Did you try to leave it unplugged and see what the temp is?
Also, are those strip thermometers accurate? I have a digital one and I've heard strip thermometers for other things, such as my ball python, are not accurate.