[ca44]

Hello Everyone,
I purchased this car last summer. It had a blown head gasket and a non-functioning water pump, plus a few other (not as serious) problems. Car only has 78k original miles on it.
Anyway, after fixing the 2 major problems I found an unfixable leak in the radiator and replaced it with a new rad and coolant temp sensor and hose from PP. I can not see any coolant leaks now and the engine runs smoothly.
So here is my problem. When I am driving the car the needle on the engine temp gauge is in the middle. I'm assuming that's normal. However, when the engine is idling, not moving, the needle will steadily move up until both fans kick in. The fans run for a few minutes and the needle comes back down to the middle mark.
It stays in this up and down cycle.
I have bled-out all of the air (I think....) by letting the engine warm up until the coolant is hot, loosened the top bleeder bolt and squeezed the top rad hose until no more air comes out of the top bleeder bolt and coolant starts to come out. As I am doing this I can see the level of coolant in the reservoir go down.
My question is - is this normal behavior? Shouldn't the engine temp stay in the normal range when it is idling? Is there another sensor that is involved in this behavior that I should be aware of?

Thanks in advance to anyone offering assistance.