a bad thermostat usually makes the engine run cold if it fails.
Happened on a toyota once where the water pump failed, choking the internal circulation of the coolant and made the temp rise almost to the red zone, then dropped back to normal after a while. From what you've said it seems like something gets stuck that chokes the internal system and blocks the heat in the cabin as well, and when the normal process resumed the engine heat got back to normal as well as the circulation in the cabin was back to ok. check the schematics as to how the war air is pushed into the cabin, perhaps the inlets are somehow blocked into the cabin and creates additional heat in the engine area. just a theory !
good luck.

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