On a gas furnace does the relay hot black wire go in the same terminal as the black hot wire transformer?

We are trying to get the furnace to turn off at the temp. the theromstat is set on. It has been running & not stopping on it's one We have had to use the circuit breaker to turn it off & on. My husband recently put a new transformer & relay in it & after doing that it won't stop running. So he is... show more We are trying to get the furnace to turn off at the temp. the theromstat is set on. It has been running & not stopping on it's one We have had to use the circuit breaker to turn it off & on.

My husband recently put a new transformer & relay in it & after doing that it won't stop running. So he is changing the wires in hope that this will fix it.

Anyone have any knowledge about these wires? He has 2 black wires---one from the relay & one from the transform, tied into the hot.
One wire at the relay comes out & goes into the furnace. There is a set of wires from the furnace that feed into something that is not related to the 120 coming in.
When he rewired this he must have done something wrong that caused the furnace to not turn off anymore.
Before he did any of this they furnance was going off & on every few minutes. It all started when he put a new thermostat & the thermostat is fine now except that we can't control the off & on button & the temperture.

thank you very much!
Update: EDIT someone told my husband to take one wire at a time & disconnect it to see if it would keep running. Is this a safe way to find out which one is operating the thermostat?
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