Heat rises, so the hottest part of the room will be above the heater when it is on. This would account for the temperature spikes. Move the heater at least 6 feet away from the incubator and if it has a fan, do not point it directly at the incubator. Washing the incubator before you use it is good, just let in run for at least 24 hours with no added water to help it dry out. You can put a plate of dry rice in it to help absorb the excess moisture.
You should get a back-up hygrometer (or 2 or 3) to check the accuracy of the digital one on the incubator. A couple of extra thermometers are a good idea, too. (ETA - I haven't had my coffee yet!) Good luck with your hatch!