I would probably say that its your thermostat. Every car has a thermostat, some people think its safe to run ur car without it, but honestly its not. Umm...and ur car shutting down could be because when u use ur air condition, the a/c compression is turning with the engine. So its using up so much juice in your battery to run the a/c as well. My car doesn't shut down but it loses power in acceleration when i have the a/c on. If not the power of the battery and it being really hot outside it could be that the flow in your cooling system isn't flowing correctly. You probably haven't done a flush or Radiator change since 1988 so you might want to do a flush then if the problem still persists then you'd want to get a new radiator, but I believe my best bet would be a flush that something its clogged in the cooling system. REMEMBER: NEVER OPEN UR RADIATOR CAP WHEN UR ENGINE IS HOT!! pressure build up inside will shoot out boiling liquid.