My '97 SE stalls out generally around the time the engine gets up to full temperature. It can be coasting at 0-35 mph or it can be idling in park and in either case its like the engine just turns off. Any ideas?

I can start it back up again right away (while coasting I throw it in N, start it back up, and throw it back in D and keep going) but it generally has a hard time maintaining idle without stalling out again right away unless I hit the throttle some. Generally it only lasts a maybe 10 seconds and then its fine from there on out...but its rather dangerous when I loose power steering and power brakes while I'm driving...

Seems like a fuel pump or fuel/ignition problem. Rest of the car seems to work fine while all this goes down. My car still has lots of power and only 125k miles.