I used an exact replacement (one can't even tell they have been repaired) and they no longer crash, no matter how hot it gets; it is indeed a permanent fix. I remain indebted to Securifi for telling me the solution; once repaired they are delightful units.
Now it might be argued that the original problem took time to show itself and that the same might be true for the replacements, but so far all is well.
One (black) unit was left in the Sun and was almost too hot to touch, but it just kept on working as if it didn't have a worry in the world.