finally go fly and now we freeze (172 air leaks)

My 172 M has some pretty big air leaks from behind the plastic pieces at the top of 
the windshield. It is coming from behind the
trim piece that encircles the vents and drops down the doorpost.

I don't see any point in caulking. It would just move the problem.

It ain't gonna get any warmer for a while so any ideas would be appreciated. (my wife 
won't move, so Florida is out for now)

Mike Z