A very long-shot, but could it be a fuel-supply problem, as in something (dirt / rust / water / old seal / ...) that partly blocks the pump, supply-lines or injector distributor (does the 348 have one of those?). When the motor is cut, the fuel pressure drops and the impurity then settles out of the way until next time it is picked-up??
I'm not sure how your "overheating" sensor system works - if the motor is NOT actually overheating it should run fine unless a faulty sensor triggers some action. Partial-firing on some cyls doesn't sound like the action I would expect to be triggered.