My furnace has been leaking water into the recess in the floor for a couple of months. It has gotten progressively worse. I had a repairman out last night and he could not find any leaks. He did shut down the valve that lets fresh water flow into the furnace. I have baseboard heat. There was no water in the recess when I checked this morning. I was worried that the furnace would run dry so I opened the valve to let fresh water flow in. Then I shut the valve again. I checked everything about 30 minutes later and there was some water in the recess again. Where could the water be coming from?

I assume by saying "furnace" you mean "hot water heater tank", correct ?

If hot w/h than: Leak could be coming from number of places:

1. tank itself
2.nipples on top ( water drips through insulation around the tank and shows on the bottom)
3. water heater flex connector
4. T&P valve at the threads
5. Thermostat / at the threads

Open water to the heater and observe / listen what's happening. See where water drip starts coming from. Follow that drip upwards until you find its source.

Come back with results and will will tell you how to proceed from this point on... Back to you... Milo

Sounds more like a boiler than a water heater. Wartmanni can you clear this up for us. When your system is running what pressure do you read?