I get hot water from the cold water faucet for about 10 - 20 seconds before the cold kicks in. Could it be the faucet? It is an old 2 handled industrial style faucet.

Does this happen year round? Your cold supply could be passing too close to a heat duct or other source of heat including the water heater. Can you trace the pipes and find a warm spot when no water is being drawn?

I get hot water from the cold water faucet for about 10 - 20 seconds before the cold kicks in. Could it be the faucet? It is an old 2 handled industrial style faucet.
I don't think it's your faucet or even a cross connection. Feel the cold water inlet pipe to your heater. Is warm to the touch? Even though it's a cold water pipe the water's warm in the pipe. This is called convection and that's what I think's happening here. Regards, Tom