I'll bet a cup of coffee that the terminal, red and white, wires are wired backwards.
The #1 terminal wire goes to the idiot light on the dash, it is the exciter wire and tells the alt to start producing juice. When the alt isn't running it provides an internal ground for the idiot light, the other side of the idiot lifgts is tied to a switched 12v source. When the engine starts and the alt starts producing juice the internal ground is removed and the idiot light goes out etc.....
The #2 terminal wire is the sense wire and is tied into the hot side of the wiring harness. This tells the alt to produce more or less juice, depending on the demands of the electrical system.
The large studded terminal on the rear is the charge wire and goes directly to the pos post on the battery.
Sense your's got hot..... bet you that it's grounding internally, even when not running.