My Hampton Bay Fan turns on in the middle of the night when I am asleep. Does anyone know if there is any way to fix this problem?

Something may be interfering with it. You need to switch to a different code. Both the remote and receiver have 4 tiny switches. They need to be set alike, but different from any near by fans or other things.

These tiny switches are called the "dip switches". The ones in the remote are, well, in the remote. The ones on the fan will either be on top of the motor, in the switch housing, or in the canopy.

More information on ceiling fan remote issues here:

http://www.ceiling-fans-n-more.com/ceiling-fan-remote-controls.php