Are temperature fluctuations bad for my fish?

I have a 5 gallon aquarium. I bought it as a kit. I currently have 2 small 1-2" fish. At room temperature (no heater) my aquarium hangs at a constant 78 degrees. the tank came with a 15 watt clear incandescent bulb. I usually turn the light on during the day (8am-8pm). The light puts out a decent amount of heat and the temperature in my tank rises to just shy of 82 degrees. 78 degrees is an ideal temperature for my fish. While 82 degrees is just barely still in the comfort zone for my fish, I am worried that this 4 degree fluctuation in temperature every 12 hours is bad for my fish. They are new and still getting used to the new tank. I don't want the shock of temperature fluctuations to cause them to croak. Does anyone know if this fluctuation is harmful for the fish? Is there any type of aquarium bulb out there that can screw into the same socket as incandescent yet produce less heat? Currently have albino cory and xray tetra. Plan on adding one additional small fish. Anyone please help. I don't want my fish to die. Is there anything I can do other than lower the temperature of my home. I would also prefer not to have to keep a fan on it during the day. Other than temp, other factors are normal. Ammonia 0, nitites 0, nitrates <5, and my fish seem to be doing ok. Just recently got them to start eating.