Atmospheric Density Required for Mercury´s Polar Regions to be Warm?

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snorkack
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TL;DR Summary
At which atmospheric density would Mercury´s poles be neither hot nor cold?
Venus has a dense atmosphere (about 90 bar).
Although Venus has a low axial inclination and the poles of Venus are therefore always in twilight, the day side atmosphere heats to about +460 C and the heat transport at the 90 bar atmosphere is so efficient that the poles are no more than 10 C cooler than day side.
Mercury has a thin atmosphere.
Day side of Mercury heats to about +430 C; but the poles are only around -170 C because of thin atmosphere and weak atmospheric heat transport.
At which atmospheric density would Mercury have just enough heat transport to provide for +20 C at poles?
 

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