1999 Ford Taurus Bad Fuel Pump?

First off, when I start my Taurus, the RPMs usually jump up to 1500+, I'm not sure if that has anything to do with my problem or not. The main problem I'm having is that my car will start and run fine for a while and then it will just die while I'm driving. It seems that most of the time it happens when I am letting off the gas (coming up to a light or going down a hill). Then if I wait about 30-45 minutes and it cools down it will start back up. I took it in and they said they were having problems getting it to stall out, they finally did and said it was a faulty fuel pump and was gonna run $1000+ to fix possibly, which seems pretty steep. Anyhow, it doesn't seem to me like this could be a fuel pump problem since it only seems to happen when the car gets warm. The problem has happened on nice days too, I drove it for a while on cold days and the car didn't die. Any help would be much appreciated, thanks in advance.