I'm not there, but I can guess, at least.
Your tank has a pressure sensing switch which might not be working correctly. Either the electrical part or the actual pressure sensing part might be stuck in the "pump-on" position, keeping the pump running even though there is enough water in the tank.
The pump, if it is staying on, is going to continue to try to put water in the tank even though the tank is full.
Closing the valve on the pump won't do anything to the switch, so the pump will continue to run even if the valve is closed.
When the pump is running, electrical power is being used to turn the pump. The energy being used to turn the pump has to go somewhere. Usually, the water keeps moving past the pump so the energy is carried to the tank, ever so slightly heating up the water in the tank. If the water is stuck at the pump, however, the water will be accumulating this energy and after a while heat up so the pump will feel hot.
Basically, if the pump is running but not moving the water, the water will slowly heat up.
You need to get someone in there who normally works on home fire sprinkler systems to fix the problem because right now, your house is not protected from fire.