While messing with my fuel pump and FI I happen to touch the voltage regulator and noticed that it was warm. The car had not been running. The battery is hooked up.

The next day the battery was dead. Should the Voltage Regulator be warm? Could this drain the battery, or do I have another problem?

Remove the alternator and have it checked out at a FLAPS; they'll tell you if it's internally shorted. It might not hurt to replace the VR with an electronic-type unit (Borg-Warner, part # R588) while you're in there.

If all checks out good, and you haven't had any other electrical gremlins, you'll be hunting down a current draw somewhere. Maybe you left the radio on last night?