After I am driving for a while (never when I start up) my Toyota Corolla '04 makes a brief high pitched squeal. No check engine light goes on and squeal goes away after about 3 secs. A/C belt? Some time ago, when my a/c switch failed, I left the a/c in the "on" setting so as to not wear out the switch. Maybe this is stressing out the a/c belt?

It could be the Bendix inside the starter which engages the
starter drive.

It could be due to a belt loose or some pulley and once the bearing heats up the squeeling stops.

Need to check the ground path on the squealing relay. A poor ground will cause this condition.

it is the belt it is either to tight or not tight enough

You need new brake pads . it has a metal tip that squeals on the rotor when they are worn.

Check your belt. Belts will whine when they're worn, cracked or glazed. I hope this was helpful. It's not normal. Take care and God bless.

Bryon

I assume the car is a petrol! to stop a petrol engine the ignition needs to be shut down! if there is over run happening there are a few reasons for this. There is a problem with ignition mudule! spark plugs coked up! or the cylinders are coked.
If the car is a Diesel model then the reason for this happening is the shut off valve on the fuel pump is at fault.

Hope this helps.

check the alternator drive belt,it may be loose and squealing.
the alternator itself could be also making a noise.
start the car with the hood open and listen to it.
look if the belt is cracked,loose or wet from oil or water etc.
things like thermostat housings leaking coolant can cause something like that.

have Your alternator belt checked for the propper tension:]

it sounds like who-ever put it back together again never tensioned your alternator belt properly and thus when its cold you hear squealing. The hum could be the belt rubbing off of the timing belt cover if that was also put on incorrectly i would think.
It would be beneficial to have it all rechecked before driving it again just to be on the safe side.