Stall at idle?

Usually if it is a sensor problem, it would throw a code. The explanation of the cold and hot sensor seems to be opposite of what I know off.
It should be the other way round.
Have you checked the Engine Coolant Temperature sensor?

It can be anything from hard starting to stalling coupled with difficult restarting.
The ECU monitors the ECT to enrich the running when cold and if it malfunctions, it could result in stalling due to runing too lean or rich.

Engine coolant temperature sensor is located in back of cylinder head.
Remove radiator cap to release pressure in system. Close radiator cap toprevent coolant feom flowing out when sensor is removed. Disconnect ECT connector. Remove ECT buy loosening with appropriate tool, being careful not to damage connector.
To install, reverse removal procedure.

I will stick by you until we can get the problem resolved. There must be an answer somewhere and hopefully we can get to it.

At 108k miles if the spark plugs had not been replaced yet, it should be long overdue. Sometimes when a problem cannot be resolved, we have to revert back to the basics and a tune-up as you are planning to do is the correct thing to start with.

Have a nice day and good luck.