Cover the entire backside...
Cover the entire backside of the damaged area with masking tape, including more than just the affected area. There should be no open seams.
Although J-B Weld is the choice for our radiator repair, it is too thick to run down and fill all the leaks, usually hardening before it runs all the way through. So we are going to modify our J-B Weld. After all, we are racers, and racers don't leave things stock. All two-part epoxies that I've used are soluble in alcohol; at least they are soluble before they harden. Therefore, alcohol can be used as a thinner and cleaner for epoxy. But it must be denatured alcohol, not rubbing alcohol.
Since pairs of 1-ounce tubes are the standard size found in stores (the company also makes 5-ounce size tubes), I picked up several packages. Styrofoam coffee cups make good mixing containers. Neither epoxy nor alcohol melts the foam. Rather than squeezing my fingers to the bone, I cut off the bottom of the tubes, making the epoxy's exit much easier. Mixing two tubes at a time, I stirred until the color of the mix was constant. Then I added the alcohol. From the 1-gallon can of alcohol I had, I used one capful to thin one pair of tubes. When stirred well, the mix has the consistency of honey. It will now pour into the damaged area of the radiator. At this lower viscosity, the J-B Weld will fill all the cracks and crevices it can reach.
After the two part J-B Weld...
After the two part J-B Weld is thoroughly mixed, there should be no streaks of color. Now add some denatured alcohol. One capful (from the gallon can) can be added to the mixture of the two tubes. Stir well until the contents of the cup are of the same consistency. With the radiator leveled, pour the J-B Weld into the wounded area. Use as much J-B Weld as necessary to fill the area.
The J-B Weld hardening time is dependent on the temperature. It is much faster at 100 degrees than at 60 degrees. If you are working in colder climates or in an air-conditioned shop (you lucky dog) consider warming the patch. The beginning of the warming procedure should have begun with the tubes of epoxy. Don't get them hot, just warm. Once the patch is complete, warm the whole area. A hair dryer is fine for this.
I mentioned setting the radiator on some blocks so you could see under it. It won't hurt to point the hair dryer under there, too. There is another advantage to having the radiator spaced up. If any epoxy leaks through the tape, it can be scraped up with a putty knife and reapplied to the top side.
Although I have never had a radiator leak using this method, I always test the radiator. There are several ways to do this.
When you make the trip to the parts store for the J-B Weld, pick up a couple of rubber freeze plugs that will fit the radiator outlets. These are the type that expand by tightening the bolt in the middle. Use these to plug the radiator outlets.
J-B Weld is used to make the...
J-B Weld is used to make the patch. Since we will be using full tubes, it will be easier to squeeze out the epoxy if we cut off the bottom end of the tube. A Styrofoam coffee cup makes a good mixing bowl. Neither epoxy nor alcohol melts Styrofoam (technically, expanded-bead polystyrene).
Method one: Use a testing radiator cap that seals against the top flange. Then pressurize the radiator through the overflow tube. If you pressurize the radiator, it must be done using a regulator in the air line. Do not use more pressure than the radiator will encounter in operation. I don't advise more than 25 psi. Once the radiator is pressurized, it will need to be immersed in water where bubbles can be seen.
Method two: Use the two plugs for the outlets. Get a good radiator cap. Using a hand-squeeze vacuum pump attached to the overflow tube, pull a good vacuum on the radiator. Pinch off the vacuum line because these little pumps often leak back. Go eat lunch, watch a movie, or something. When you return, pull the hose off the radiator. If it still has vacuum, it should be OK. A crude repair, perhaps, but it has always worked for me.
A new radiator is always best. You can often repair one if damage is not too great. A repaired radiator such as this will not cool as well as a new one, but repaired radiators make good spares.
Clean the radiator well. Use J-B Weld thinned with denatured alcohol for the repair. Test the radiator after repairing.

After blending with alcohol,...

After blending with alcohol, the mixture is about the consistency of honey. This will allow the epoxy to fill even the smallest holes before it sets up.

Look underneath the radiator...

Look underneath the radiator to see if there is a leak in the tape. If so, the epoxy that has soaked through can be scooped up and recycled to the top.

Patch finished. The area around...

Patch finished. The area around the patch is now full of J-B Weld. We have a complete plug around the damaged area. The only thing left to do is to get some rubber freeze plugs for the outlets and apply pressure (25 psi max) or vacuum to the radiator. This test will reveal any leaks.