Navier-Stokes ♥ Heat conduction = True ?

In a recent post by Claes Johnson I get the impression that Claes have now started to entertain an idea that I myself have come to regard as the most promising alternative to the Greenhouse gas dogma: Heat conduction (which includes radiation) combined with fluid dynamics, where the heat successively escapes to outer space as the atmosphere gets thinner. 

The way convection is treated in state of the art climate models seems to be rather rudimentary. Quoting Liou again:

"For applications to one-dimensional climate models, the critical lapse rate,.., is usually assumed to be 6.5 K /km for the globally averaged condition. This number is based on the fact that the climatological atmospheric temperature profile in the troposphere has a lapse rate close to this value."

Surely we ought to be able to do better than this. But the question then goes to Claes: Is it straightforward to combine Navier-Stokes equations with heat conduction, in that case how is it done and have you tried it?