I would still have this checked out, pain from a mild heart attack will after a while stop, but just because it stops does not make it something to ignore. My husbands did this on a few occasions and it was only because I called the emergency out of hours doctor despite resistance from him, that an ambulance was sent immediately to our house and they did a heart trace and he WAS having a heart attack. We later discovered when they did further tests that the previous occurances had in fact been mild heart attacks too. He had no shortness of breath, no pain in his arm, no family history or any other signs, just the pain. It is not worth the risk to ignore things like this by doing so you could be risking your life.
OK lecture over, but please get this checked out.