Thermal balance for the surface where the atmosphere absorbs most energy

The setting is a moon-sized body with solid surface, thick (but mostly transparent) atmosphere and magnetosphere. But most heat from the space is supplied with relativistic charged particles impacting the atmosphere in some regions. And only minute quantities "“ via (solar radiation)-like transport; about 1/30 the Earth's solar light energy flux. The body would be an artificial construct, but unnatural features shouldn't be very prominent. We need the surface to be inhabited, so, it may not be very cold.

The problem: how to transport heat from the atmosphere to the surface? The surface will inevitably lose heat to the outer space via thermal radiation, whereas hot air won't go down easily to compensate for it.

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Thermal balance for the surface where the atmosphere absorbs most energy

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