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This will eliminate or confirm the L8124 as the cause of the short cycle. When the thermostat calls for the L8124 to operate the circulator then the burner also operates thru the 1k1 relay contact. By having the low limit operate to 170°F with a 20° diff then there will be no reason to call for heat from the thermostat while the circulator pump operates from a separate power source. This will get the heat up to the radiators. The burner will operate as if there was no call for heat and the radiators will get hot enough the heat the house.

If the circulator pump powered by the other power source is shorting out the other power source, then we will know that the circulator is causing the L8124 to short cycle the burner. If the circulator pump operates fine from the other power source and the burner operates without short cycling when there is no call for heat, then we have pinpointed the L8124 as the problem.

You have given @ColdMainer a great test to eliminate two problems and confirm one of them.

@109A_5

If the DHW call works consistently and just the call for heat is intermittent I would suspect the aquastat since the electrical path through it is different for the different operations. 

Well stated. I agree.

This theory can be tested as follows:

1. Turn the thermostat all the way down to the minimum possible temperature. The house must be above this temperature for the test to work.
2. Turn the High limit up to 210.
3. Turn the Low limit up to 170.
4. Turn the "Diff" to 20.
5. Disconnect the circulator leads and power the circulator independently from a standard outlet (not from the L8124). The circulator will run continuously.

Observe the behavior of the boiler. See if it will rise to 170F…………fall back to 150F……….and rise to 170F again without short cycling.

Of course you cannot leave it in this condition or it will overheat the building. But, it tests the L8124 to see if its K1 relay is problematical.

ALSO: When you get finished, move the THE DIFF to 15. This will cut the cycling of the boiler dramatically. Leave the LL at 170. Move the High Limit to 190.

That's the perfect sketch, Ed. Thanks for putting that up. It will really help him.

With the power off, open the cover on the side of the circulator. There will be two wires with wire nuts on them. Undo the wire nuts and connect the leads from the circulator (not from the incoming wire) to a new cord that has a standard outlet plug on it. You'll probably need to make this cord from an extension cord. Plug this into a standard duplex outlet. Now, the circulator runs continuously, independent of the L8124

Also the relay solder joints to the circuit board in Honeywell aquastats is a known issue. The Red arrow points to the Relay. It as a much more awkward job to inspect the relay solder joints in the aquastat, much disassembly. Mechanical pressure (with an insulated nonmetallic tool) from different angles to the circuit board and the frame of the relay may identify a failing solder joint during a failed call for heat.

If the DHW call works consistently and just the call for heat is intermittent I would suspect the aquastat since the electrical path through it is different for the different operations. The Red highlight components is a thermostat call path which uses the relay the get power at B1 to B2, the DHW low limit path uses the contact highlighted Blue. If the solder connections are intermittent at K1 or 1K1 the power to the rest of the system will be intermittent too and only during a thermostat call. With a meter it would make short work of where the electrical path ends when the system acts up.