The back porch leaks water during a particularly heavy rain storm. New
shingles were put on about a year ago by a professional roofer and it
didn't leak until I hammered up ceiling boards to the inside of the
porch just recently.

On inspection, there is a thick bead of black caulking along the top of
the flashing where it lies against the brick of the house but it must
have microscopic cracks in it to cause so many leaks.

If I took a heat gun and ran it along the bead of caulking along the top
of the flashing, would it melt enough to seal any cracks? Or is it
necessary to remove the old caulking first then apply new?

Any more ideas, particularly better ones?