Unplug your compressor for a bit to see if the heat goes away. The clutch is just a big electromagnet with a wire coil inside.
There is a resistor built into the plug on the compressor clutch. It's there to bleed off the random current generated by the clutch when the pulley's turning and it's not engaged (ac off). That resistor is there to prevent excessive arcing of the contacts inside the compressor relay as the clutch is engaged. If that bleed resistor is bad (open) it could have fried the contacts inside the relay causing a poor connection.
Check your ohms to ground on the plug and on the compressor clutch itself. The clutch could be shorted to ground.