Ok, then it sounds like we basically we agree
Except, the original poster didn't have a persistent overheat condition, but a flickering light. In any problem relating to the engine, I would say that looking at the engine parameters is common sense. I have no idea if a core leak would cause abnormal engine parameters? Most likely, it would certainly not produce a flickering overheat indication, but rather directly a fire warning.
Hence, with a flicking indication and everything else looking good, I think the original poster solved the problem in a reasonable manner.