Taurus 2001 will do cold starts, but not hot starts

My 2001 Taurus will do cold starts fine after sitting at home overnite or sitting all day at my workplace all day. But after starting fine after sitting at workplace all day - - if I drive somewhere else, go inside for a little while, then come out and start car - -- the engine starts, car shakes and sputters, then dies and wont re-start. What is causing it to do cold starts -- - then when it warms up, wont do hot starts?