WHAT IS WRONG WITH MY CAR?

ok so this is what happens, When I drive my 1989 pontiac firebird round town running from place to place, after about 3-5 stops then when I try to start my car again it will not start. what is wrong with it, is it a head gasket problem or is the heating core thing going out?????? I need help to figure the problem out. i really want to keep my car. thanks for any help advice you can give.