Oldsmobile Intrigue rides for a day and cuts off (HELP ME PLEASE).

vincentvl25

I have a 2001 intrigue and my trouble started on may 20 my wife called me and said it was overheating and it wont start got it towed home after a failed attempt to jump it off next day found out the belt was off and wrapped around the tire rod . Changed the belt got a new battery all good started up 6 hours later battery light came on so I popped the hood checked everything then got back in did a u turn then it cutoff another tow home. Then we changed the alternator then put another new battery in started up next day drove my wife to work took my son to school no problem. I go home wait til its time for me to go to work get on e-way drive for about maybe 10-12 miles maybe more I looked down there go the battery light and every other light came on after that. got off parked got on the phone prepared to get another tow then I get back in the car it started I drove for like 6 blocks before it cutoff then I parked and left it and went to work. next day I went to go check on it with my cousin/mechanic and he thought it was overheating but the gauge was in the middle like its supposed to be so we change the thermastate and the reservoir it had a small leak put another new battery in started up drove for another day for it cut off again does anyone know what the problem could be or has this happen to anyone before please help.