87 firebird 350 running problems

I was wondering if anybody could help me with my firebird running problem...ok its like this I recently changed out my 305 motor for a 350 switched the ecm and everything...now the car runs good when started but if its taken on a 30 or so minute trip and u shut it off and go inside the store or whatever...come back out and start it (starts fine again) but then dies...what gives?