Welcome to the forum!
If you suspect it's a belt, you could try some Dri-Lube on the inside of the belt. That stuff has caused slipping issues in the past for some people, I've used it myself on my cars and haven't had any dramas but your mileage may vary.
Alternatively it could be a bearing. Fastest way to figure that is to grab a can of Silicone Lube (made by WD40 company, available in Bunnings etc) and put a squirt on the bearing itself, be careful not to hit the belt.
Also, give the cooling fan a spin by hand. It should resist turning, but should be absolutely smooth.
Other things that can squeak: water pump, alternator, suspension, turbocharger ... there are ways to isolate these.
Suspension will ONLY squeak when you've physically moved the vehicle so that the shocks move up and down. If the squeak happens while the car is motionless and nobody's climbing in or out, it is NOT your suspension.
Turbocharger only really starts spinning above about 1200-1300rpm. If you get the squeak at idle, it is NOT your turbocharger. If you think it IS your turbocharger, stop the engine immediately. A blown turbocharger may equal a destroyed motor if it lets go.
If the alternator is squeaking, it could get change when the alternator gets heavily loaded. Start the car, turn on EVERY electrical item (headlights, driving lights, stereo, plug stuff in to the cig lighters too).
Back to that turbocharger - if you suspect it, do the following:
* turn off the engine
* thoroughly clean your hands and the outside of the air pipe leading into the turbo
* remove the air pipe that bolts to the front of the turbo
* give the turbo's shaft a spin and wiggle.
If you can wiggle it, it's gotta come out for a bearing replacement. If you spin it and it feels in the slightest bit rough, bearings need replacing. It should be absolutely smooth, no gritty feel, and solidly spinning without any noticeable wobble at all. Oh, and do NOT start the engine, under any circumstances, if the turbocharger is showing signs of damage like this!
The waterpump will make noise at any time (regardless of warm/cold engine) so if it's not any of the others, suspect this and get someone to lend you a stethoscope to have a listen to it.
Good luck!