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I have had new dme relays fail.....mainly due to the fuel pump pulling to much current, is the relay getting very hot?
When the car stalls is the fuel pump running? The car will run for about 5 seconds after the pump shuts off.....meaning if the dme relay is failing it can cause just the pump to lose power.

But I think there is something going on with the temp sensor.....check it's resistance at the sensor with it unplugged, then check the resistance at the dme (with sensor plugged in and dme unplugged) it should read the same, if not it could be a ground issue......

Do as mentioned, with it unplugged let it idle up to warm then plug it in...and see if it gets better.....

I know for a fact when the engine is cold and the sensor is unplugged it will run exactly as you describe....