1998 Ford Taurus Car stalls after driving 30-40 minutes the

Problem started after I learned car would not start up again if I turned it off after driving more than about 20-30 minutes. Once the car cooled down for an hour or so it would start again. Problem has worsened and now it will quit while running. This occurs at a stop light and the RPMs have gotten increasingly lower at idle.750 or less and it chokes up and quits. Pumping the accelerator does not have any effect on the car and will not keep it from quitting. As if it's not getting any gas when I press on the pedal. The temperature gauge seems to be fine and I don't see other signs of high temperatures. What could this be? It's something clearly related to the car once it has warmed up and has been driven for 1/2 hour or more.