unable to restart car without resting it for an hour in hot weather

What is your question?

This problem started about 2 years ago. In hot weather I cannot make more than 1 or 2 short stops otherwise I cannot restatr the car until it rests for @ an hour. The car has about 55,000 miles on it. The battery was replaced. The temperature gauge reads normal. It's been through diagnostics at a Buick dealer 2 times and they can't find anything. My husband brought it to a repair ship and they say it's a fuel pump and want $700 to replace it. I have my doubts because of the low mileage and I cannot see why the temperature would play a role in the problem. I would appreciate your help as I am afraid to drive it. I also had the problem with the windows that one of your readers described.