My engine started overheating and belt is loose

Sounds like your pulley belt tensioner is shot, they are usually 'automatic' in that they decrease the slack as the belt wears. If the belt is in good condition aka not frayed, or has cracks or splits then it can be reused.

Usually on the belt tensioners there is a squared off piece, that is for attaching a box spanner (box wrench) to so you can manually move it in to the release position. Check the spring tension by attaching a box wrench of appropriate size and levering to see if you can feel spring tension. If you can feel good spring tension, try spinning the free spinning pulley. If it feels tight or notchy that is your problem and the tensioner will have to be replaced.