Blower motor still runs on high when ignition is turned on.
My car has 245000 miles.
My car has an automatic transmission.
When this occurs, it is a sign that the positive side of an electrical circuit has shorted to ground. In the industry, we humorously call this, "letting the smoke out." This situation creates a lot of heat and has a habit of melting whatever it comes into contact with. Whether it be more wiring in the harness that it runs through, plastic clips that hold the wiring harness in place, or plastic encased electronic components that the circuit may be connected to or in physical contact with.
Since the blower motor still runs, I would have to say that the circuit has not been affected. What is below that is the starter motor and a wiring harness that supplies power and ground to multiple systems allowing your vehicle to run. The starter area of your particular vehicle is a common problem area for wiring problems. The space it routes is tight, under exhaust manifolds that run very hot and the starter motor runs the highest electrical current of any system on a car. This is a common electrical problem area on your vehicle.
My assumption is that smoke is rising and is entering the blower motor box, making it appear there is an issue with the blower motor or blower resistor. Either way, my assumption being correct or not, you will need to do some exploratory disassembly to locate what wires have shorted to ground. I would start by looking at the starter. The starter itself has a bundle of wires inside it. It maybe the source of all the smoke.
If you need help with this, consider YourMechanic, as a certified technician will be able to come to your home or office to diagnose the smoke that is coming from your car and determine what repairs will be needed to resolve your issue.
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