If the heater fan is off, there are only a few things that I can think of;

The valve that changes the flow into the heater caore, which adjusts the interior heat, might not be closing all the way and creatting a high pitched noise.
The thermostat might be stuck partially open and stuck in a position it does nto normally operate in which could cause a high pitched noies.
Resonance from interior metals or engine bay parts could vibrate against each other and casue noises.
There could be worn out accessory belts that needs replacement or adjustment.
The power steering level may be low.
The timing chain/belt could need replacement.

Check out those possibilites and maybe try to see where the noise sounds like it is coming from if the hood is open and you look around for its source.

Answered by DrCranknWrench (expert)
3,292 answers provided