Maybe some of my smart readership can help.

It quit working the other day. I went in and looked at it, and the wiring from the thermostat had lost all its insulation and was extremely oxidized--it looked like a long, anorexic green worm. I figured the problem was that it had quit conducting, and replaced the bad sections with new wiring.

No joy.

I've an electronic thermostat (about ten years old or so), and it indicates that it's working (the temperature LCD flashes when it's supposedly telling the furnace to burn). I've always thought that the voltage on these things is supposed to be 24VAC, but when I disconnected the wiring and measured it, it was only fourteen. Is this indicative of a problem? Is it possible that the wiring was OK, and that I have a different problem? Like a bad thermocouple?

Does anyone have any theories, and experiments I could run?

Sounds like it may be a bad controller board at the furnace itself - that's where the thermostat trigger voltage is generated. Just curious, is the thermostat a Honeywell? They get operational voltage via the furnace control board; many other electronic (esp. programmable) thermostats are battery-powered, and sometimes the battery(s) aren't obviously placed in the thermostat case.

Shorting the wires at the thermostat should tell you if it is working. Shorting the wires at the furnace should tell you if it's the wiring.

Gas or oil? Could be bad sensor or clogged fuel line. There are a few online forums to help if you have specific info on make/model.

The thermostat does have AA batteries in it. I think they're working, because the display is doing what it should. I'm seeing the same voltage at the thermostat as I am at the furnace (about 14VAC) so I think the wiring's OK at this point. When I short at the valve end, the furnace doesn't come on.

Oh, and it's gas, and the pilot is lit.

14 volts from AA batteries? Shouldn't the total be a multiple of 1.5?

Come to think of it, getting 24 volts from a series of 1.5-volt batteries requires 16 of them, and that's ... too many.

Therefore I rather doubt it has to do with the batteries. FWIW.

It doesn't get fourteen volts from the batteries (I said it was AC). It only gets a volt and a half (they're in parallel). The AC voltage comes from a transformer at the furnace. The batteries are probably just backup for the clock in the thermostat.

The oxidized wiring and missing insulation indicates high impedance or an overcurrent condition.

If you're going to repair a gas furnace yourself then up your life insurance and then plug the make/model into Google for diagrams/parts.

It might indicate that, all else being equal, but the wiring that has the problem is very close to the burners. As it gets farther away, the problem disappears. If it were caused by an overcurrent, I suspect that it would be attacking the whole length of the wire, not just the part near the heat.

The valve is one that I've had to replace in the past (a few years ago) due to similar overheating. It's a lousy furnace design. I'd replace it with a newer, more efficient one, but it's hard to ecomomically justify in Southern California--my gas bill's just not that high.