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The heat will transfer through the casing a lot. Then you have the different CTE between the metals. It cant contract with temperature, it just wont expand as much if the outer isnt able to move (not as hot).
No, it's not increasing and shrinking at the same time.
http://physics.bu.edu/~duffy/py105/Temperature.html#:~:text=So%2C%20with%20something%20like%20a,same%20material%20as%20the%20hole.