A giant steel rod hanging from moon with its other end in atmosphere

Assume there is a giant steel (or any metal with good thermal conductivity coefficient) rod hanging from moon with its other end in atmosphere (say 5KM above sea level).

1.) Being the other end of rod is in space where it is really cold, will it help in any way to transfer the heat from the atmosphere to space?

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A giant steel rod hanging from moon with its other end in atmosphere

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