RE: Cleaning tranny cooler
There is a good product called Kooler Kleen. It comes in a pressurized can and it's about 10-12 bucks a can. You can get it at NAPA or Carquest parts stores.
Use 2 cans of it. Disconnect the lines at the transmission and the can has a hose and fitting to connect to the line. Start blowing the stuff through until it comes out the other end and let it sit in there for about 15 minutes. Then, run about half a can through one way and the other half through the other direction. Do the same with the other can.
I use an air compressor and blow the lines dry between cans and when I am done with the last one. Be careful with the compressor so that you don't use too much air pressure and rupture anything.
It works great and doesn't take but just a little while to do.
If you are really worried, a replacement radiator is not as much as you probably think and well worth the investment. I have found them on eBay auctions regularly for less than $100 brand new.
Whatever you do, get the thing clean or replace it. The leading cause of a second failure is contamination left in the system from the first.