Harry,
Keith is right if the radiator isn't really packed full of oil/soot coated debris. The shop I use had pulled a rear radiator out of a 2000 Contessa that didn't look like it had ever been cleaned. Only area for air flow was the fan radius itself. Rest of unit was packed with debris and coated with the diesel soot, etc from the engine blow-by, which should have been re-routed. It clearly had to be removed for steam cleaning. Suggest you run engine at high idle and check for airflow at the radiator. If you have a few areas, (normally corners) where it is reduced, you may be able to clean it yourself. I'd use air first to blow out as much as possible before going to water and detergent. You might want to try Dawn instead of Simple Green as there was a thread on he forum earlier about Simple Green affecting aluminum if not completely flushed. If you can't get it clean consider having a shop steam clean it. Pulling it will be a real job, that I'd try and avoid unless it was absolutely needed.
Good luck, Steve