"When the battery was temporarily reconnected again, the strange whirring sound came back immediately, but this time the speed of the whirring kept changing as the source of it seemed to randomly spool itself down to a near stop, then back up again.
This was all happening with the engine off and the keys removed from the ignition."
This part sounds like the high-speed cooling fan which can run for a few minutes after the car is switched off, especially if the air conditioning has been on.
A sticky relay is often the cause of it continuing to run & cycle up & down.
It should be fairly apparent if it is that fan or the power steering fan which is easily visible underneath the engine.
I can't explain the smoke, though.
This was all happening with the engine off and the keys removed from the ignition."
This part sounds like the high-speed cooling fan which can run for a few minutes after the car is switched off, especially if the air conditioning has been on.
A sticky relay is often the cause of it continuing to run & cycle up & down.
It should be fairly apparent if it is that fan or the power steering fan which is easily visible underneath the engine.
I can't explain the smoke, though.
