I have a 2001 montero sport 3.0 that runs great but makes a shreaking noise when accelerating, especially on hot days. The noise stops when I take my foot off the accerator and also stops after a while.

 

Sounds like a classic case of a loose belt. Check to see if there is a lot of slack in any of the belts. You can also verify by getting a can of spray belt dressing and giving the belts a squirt one at a time until you find the one that is squealing. The dressing will help for a while but you need to have them tightened or replaced soon.

Ron