Hyundai excell 1998

I’m hearing an unusual noise that sounds like a rattling or clancking sound under the fender of the passenger side of the vehicle…it has no order to the noise like when I brake or turn,etc. it just decides to do it when it wants to.

Possibly an exhaust heat shield rattling. That would likely be an inexpensive thing to have repaired.

wouldn’t my car over-heat? because it doesn’t unless I’m in traffic a long time in the middle of summer-otherwise it stays cool.

No. The heat shields around the exhaust system are simply pieces sheet metal that protect other parts of the car from the heat of the exhaust system. Being pieces of sheet metal, they are prone to rattle. They have nothing to do with the temperature of your engine.