Engine dies but eventually starts back up

I have a 97 900SE turbo convertible that has some problems. I bought it from a guy and drove it about 100 miles. I pulled over and let the top down, left the car idling. I then proceeded to leave. I drove about 100 feet and the engine just died. I cranked it back up and drove off again and it did the same thing. I cranked it once again and it drove fine. The next day I drove it about 2 miles and it did the same thing except for this time it acted like it was out of gas. After trying to start it up a few times I was finally able to drive off. During the start up process the car would idle but when I put it in drive and try to leave. It has done this now everytime that I drive the car. I can led it idle and it will eventually die. But like I said, I can eventually get it running again. It sounds to me like something is heating up (electrically) and eventually cooling off. Does anyone have any ideas.