Why does my kitchen faucet's handle get hot while not in use?

Hot plumbing fixtures can mean an electrical problem. There's enough leakage current to make something warm but not enough to trip a circuit breaker. The fixture is close enough to ground potential to not give someone a shock. One way to test for this is to cut power at the circuit breaker to any circuit that is near the kitchen plumbing. If this keeps the faucet from warming up then keep the circuit off and call an electrician.