Here are the symptoms:
1. Unless the engine is warmed up for awhile after starting, it will stagger and try to die for several blocks unless given LOTS of throttle.
2. Even when warm, it stumbles on hard acceleration until it gets above 3,000 rpm, where it smooths out.
3. Sometimes the engine light comes on for no apparent reason and it starts to run horribly - until I restart the engine, then returns to normal.
4. Another thing that will bring on the "engine light stumble" is switching from one HVAC mode to another - say from Max AC to Defrost. Again, the reliable cure is a restart.
5. The only clue I have is that I pulled into my mechanic's shop with the engine light on and the car running like crap and he found a code indicating that the computer apparently thought it was -35° F!

He wants to blame the ECM. I have a spare ECM, but I would rather not hook the damn thing up just to see if it's the problem - especially if more knowledgeable folks here can suggest something simpler to try first. Thanks in advance for any help you can offer!

What year duke are we referring to?

If the computer thinks it is -35 degrees, then there is an issue with either the temp sensor, the ECM, or the wiring between the two.

First, I would test/replace the temp sensor (ECM sensor, not the fan or gauge sensor). If that doesn't solve it, I would pull the center console and check continuity between the sensor and the ECM. If that checks out good, then swap the ECM (after all, you are already into the car that far, that is an easy next step).

You said it goes away when it warms up. Is it really temp related? Or does it go away when the car goes from closed loop to open loop?

Edit to add...My first though was the ground wire to the sensor. On an 84 (don't know if it is the same on other years), that is the same ground as the TPS sensor...which would explain the warm issue too. But....if this was the case, you would most likely get a code 22 (TPS low voltage).

Edit to add again...If it were a coolant sensor issue, you should be getting a code 15 (coolant sensor high voltage) if it is giving a reading that low. So...next thought is the wiring issue (I think no signal from the temp sensor would be read as -35)...but I would then expect a code 45 (O2 rich). Hmmmm....I am thinking your mechanic may be right...but I would still troubleshoot in the order I listed earlier.

[This message has been edited by CowsPatoot (edited 07-19-2013).]