Today I argued that heating and cooling a metal many times will affect its thermal conductivity. My idea is that heating and cooling, ie. thermal fatigue, will affect longterm the the microstructure of the crystal, perhaps form some cracks, and the same piece of metal will not have the same thermal conductivity. Is this true? In what extend? I don't recall seeing metallic pots for cooking, to increase the time of cooking if they get old. Any hint?
It's really unanswerable. Defects in a metal do decrease its thermal conductivity, but heat can either cause stress and create dislocations (because application of heat causes temperature differences inside the material) or can cause annealing (the crystal structure can 'relax' to near-perfect, and erase the dislocations).
In electrical solder, heat can also dissolve copper wire into the tin/lead alloy, and THAT embrittles the metal considerably. Mostly, metal pots aren't made of such thermally-unstable stuff.