My cold water heater's overflow outside drain pipe has been running hot water out of it non-stop. I turned the inflow water valve to the water heater off and the water stopped running. But what is causing this water to flow out like that?
Since your question says hot water, not steam escaping from overflow, my first thought would be to check for a faulty high pressure relief valve. This is the cylinder with the little lift switch usually mounted atop the tank with the drain line attached.
How old is the water tank?
It could be rusted through the internal piping and water is finding a way out.
In our experience it doesn't matter the water quality. I live in the city where the water is softer and my parents are in the suburbs where its harder. If its going to rust, the water will find a way through.
Check the temperature also; if its to hot, expansion could be causing the water to get through somewhere; which would probably tell me its time to replace it anyways.
In the last days of ours, water was trickling out of the top where it feeds the house at the connection between the heater and the copper pipe.
In our case the tank was in excess of 10+ years and in my experience, they don't last much longer than 7 (your average GE tank from home depot or lowes)
It might be time to replace it.
If you do buy a new one, keep the paper work and we also mark the month / year we replaced it on the tank now. My father replaced his after just 3 years, called GE and they sent him a new, top of the line one because he could produce the receipt and paper work and it was within the normal operating period for the tank.