Ideally, you follow the IPC reflow profile: Roughly 3 minutes of pre-heating at 150 deg C, then ramp up to 260 deg. air temperature and make sure that you don't expose the board to this temperature for more than two minutes. I just keep lifting on the chip with tweezers while I apply hot air, and I move the hot air away as soon as I have the chip off.
Don't force cooling, but let it cool in free air. You should solder the new chip on with a normal soldering iron, not with hot air, as that means less stress for the materials.