If you can’t fix it with a hammer, it’s an electrical issue.
Trust me. I’m an electrician
Anyway, IIRC the 96-97 Cobra kicks the fan on low speed @ 208* and off @ 200*. It turns the high speed fan on at 228* and off at 224*. It should also turn the high speed on when you turn the AC on.
-It’s possible that you have a defective sensor.-
The fact it runs when you pull it tells me the system runs in a “fail closed” condition to prevent engine overheating in the event the sensor failed, which you simulated by pulling the plug.
How about some questions?
Does the fan kick into “high speed” when you turn the AC on?
Do you have an old, but functional sensor you could try?
What other factors are you forgetting that could've led to this situation? Any recent maintenance or upgrades? New tune?
200° isnt hightemp. Factory temp is something like 220°
Park on steep hill, nose up, run engine
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This will help with the burping, or you can use ramps/jack stands and chock the rear wheels.