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The most likely cause of what you describe would be a short in the thermostat circuit or perhaps in the gas valve itself. You may have inadvertently corrected it when you cleaned. I would just keep an eye on it for now. If it doesn't act up then it's probably OK. It would be tough to pin down the cause if the problem is intermittent, it's next to impossible if it doesn't act up
I didn't put down that the intervals were in seconds, not minutes, so that it turned on and off very rapidly, enouhg to wake me up at 1:30 am. Same answer? Would the gas valve you mention be the one in the unit itself?
Yes the gas valve is the one in the unit itself. Your clarification does open up a few more possibilities. You could also have a faulty limit switch/sensor or a failing thermopile (similar to a thermocouple). If my memory is accurate you unit has a thermopile (2 wires from it connecting to the gas valve where a thermocouple would have one bare copper wire). But the intermittent problem issue remains
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