After an hour of being on (while I was testing and playing with it), it got really, really hot.

How much current does it draw? After all, 14-5=9V, and if it draws 1A that is 9W of heat...
IIRC you're using a 7805 regulator? What package is it (TO-220, ....)?
You can drop some of the voltage over a resistor or a number of series connected diodes to redistribute the heat generating, or attach a heat sink to the regulator. Putting the circuit in a small aluminum box and bolting the regulator to it should be enough (beware of which terminal the regulator case is attached to though...) Another option (more expensive) is a switching regulator which is more efficient.

/Michael