I just bought this car and runs great, yesterday after coming home I heard the engine fan running, didn't give it any thought because I knew this was normal. went outside about an hour later still running. turned the car on opened the heater all the way. I had already filled the radiator with antifreeze, but did fail to check the overflow. fan stopped few minutes later. it should be noted it was the drivers side fan that was running. Later that night I went outside to go to the store and the battery was dead.

I would appreciate which direction to go

 

That the A/C fan. I would surmise that the fan relay is stuck open. You need to test the relay for proper function. It's in the underhood fusebox.

 

sounds normal. You sometime walk out of cars and the AC is going off to cool off?