1993 Honda Civic Recent Overheating. Car Idles High &

My 1993 Honda Civic DX recently overheated. After filling the radiator reservoir & letting the engine cool down, I drove the car home. The next day, with the engine cool, I was unable to get the radiator cap off, but the level in the reservoir was good, so I drove the car. When the car is in park, or neutral the engine constantly idles high, then low, high then low. This doesn't happen when the car is in drive. The temperature gauge stays in the normal range, for about 10 - 15 minutes of running and then it shoots all the way to Hot. This is despite the fact that both the coolant and oil levels are normal. What could be causing this?