I don't know how much the '39-'40 is different from the '36-'38, but my original '37 radiator was a non-pressure I had converted to a pressure system. I ran a 4 lb cap so not all that much pressure. Every time the engine was started from cold, the top tank would POP when it was heating up and getting pressure on it. This lead to cracks at the solder seem. About once a year I would pull it out and solder the seem shut and go again. I finally replaced it with a AFCO brand aluminum which at the time was pretty good investment. Mine sets forward and down from factory due to the 250 inline six, but it did match up to the original. I altered the side plates to fit my truck. I still have the AFCO but wouldn't buy another one, the tubes are epoxied into the end caps. I would want a fully welded aluminum or soldered brass next time. I fixed a couple leaks with some 3M epoxy that's been holding so far.
Clean the leaking area with a stainless steel brush and make sure it's dry, then use a soft flame propane torch or if you have one a solder tip for a propane torch and just repair what you have. With the solder tip, no flame hits the tanks and the heat is much easier to control. I found it to be pretty easy to fix them.
On a side note, when I changed out my radiator, I wrapped the old one in heavy cardboard and put it up on a shelf out of harms way. I decided to sell it off to guy needing one and pulled it down to ship it. The top tank was totally destroyed, looked like it was shattered glass yet the cardboard was even scratched. All I could figure was the old brass just gave up and came apart from all the flexing, it was really thin.
