The process described below is only used for a last resort - to rescue an old-style brass/copper radiator - I wouldn't waste the time on the new aluminum ones with plastic tanks.
Due to fitment/application issues with aftermarket units, I have been soldering my OEM (brass/copper) radiators for awhile now.
It really isn't as big of a deal as they make it seem. And, as long as the watersides are clean, they are worth saving.
But, even if the internal passages are restricted with deposits - don't immediately junk it. These radiators are extremely heavy duty and can be chemically cleaned using a good CLR type product (ZEP's Calcium Lime & Rust Remover is outstanding - and cheap at Home Depot).
The cleaning process goes something like this:
I have used CLR and Bar Keepers Friend (the BKF needs to be mixed with hot water to get it into solution) to clean radiators several times with no ill effects.
I started doing this because the radiators were original - OEM with brass tanks and copper tubes. They were beautiful - had no leaks and the fins were all there. Looked great from the outside.
But inside was another story, the tube ends (where they are soldered to the tanks) were so fouled that flow was being restricted. The watersides of the tanks were encrusted with deposits as well (so the assumption was that the inner walls of the tubes were in similar condition).
There are no more radiator shops around here, so I decided to "boil" them out myself. Nothing to lose; otherwise they would have certainly just been junked.
I have only done this with the radiator out of the truck and lying flat (outside and on a wooden picnic table). Radiator cap is on and the small connection to the expansion tank is capped
Pour a whole quart of CLR into the radiator and top off with city water. I use ZEP brand - it has a higher concentration of acid (hydrochloric & sulfamic) than the big name brand. If using Bar Keepers Friend (oxalic acid) mix half a can of powder into warm water and stir until you have a solution that can be poured.
Let it sit for hours. When you want to check the progress, dump the acid/water out (save it in a bucket - it still has plenty of life). Using a garden hose at full flow, flush the waterside out. Go in both directions. Lift and shake a couple of times. When no more deposits are getting flushed out, pour the acid back into the radiator. It helps if you filter the re-used solution through a piece of window screen or similar.
With several applications (dump and flush with clean water between) the deposits will be gone and the copper and brass will be a golden color.
When satisfied that you have clean surfaces and will get good heat transfer/coolant flow, do a final long flush to get any remaining acid out. If it makes you feel better, you can use a solution of baking soda/water to neutralize.
As for repair, you're lucky; the area where your leak exists is the part of a radiator that has the greatest chance of being successfully fixed. The metal is at it's thickest there and can be easily accessed.
The soldering process varies depending on where the leak is. But wherever the repair is to be done - success is all about preparation.
If the work that is going to be done is on the heat exchanger section (i.e. on the tubes/fins, as opposed to on a tank), carefully cut away the fins in the surrounding area to expose the repair area.
Use a pair of scissors and a utility knife. The reduction in BTU rejection capacity - due to removing a couple of square inches of fin - will be minimal.
Clean the area to be soldered with a wire brush (brass bristles/toothbrush sized is great).
After using the wire brush to meticulously remove any paint, oil/grease or leaked deposits, use a solvent to further clean the repair spot.
Wash the entire area down with a solvent that leaves no residue. I use Brakleen (red not green) but carb cleaner will work - as will acetone or MEK.
NOTE : AFTER USING ANY FLAMMABLE SOLVENT TO PREP THE AREA FOR SOLDERING, IT IS IMPERATIVE THAT THE RADIATOR BE BLOWN OUT WITH AIR TILL COMPLETELY DRY. IF ANY REMAINING SOLVENT IS EXPOSED TO THE TORCH FLAME IT WILL FLAME UP AND MAY EVEN EXPLODE!
After the area is clean, liberally apply flux. Be sure to brush the flux down into the crack/hole. Use regular 95/5 plumbing solder for this process.
Then, using a propane torch with a small tip, gently apply heat to the repair area. Keep touching the solder to the tube (or tank as the case may be) until it flows. Remove the flame and fill the hole with solder. Only apply more heat as needed.
When the crack/hole is filled in and covered over, bring the flame back to the repaired area and reflow the solder one more time.
Fill the radiator with water and check for leakage.
If desired coat the repair and surrounding area with Rustoleum's Rust Reformer.