There is a heat conductive paste available, at welding shops, and gunsmith supply houses like Brownell's, that is
made especially for this task.  It will let you weld longer than the wet rags will allow.

   Most emphatically, I would not weld anything "pressure critical" with water in the tubes.  To protect the joints between tube and fin, the paste can even be worked into the fins, and then washed out with hot water later (some will run out from the heat of welding).

Regards,
Dale R.

Thanks Dale.  That sounds like just the ticket.  In a quick search, it appears that this stuff is used for plumbing work, so maybe I can even find it at Lowe's.