Not sure where your title comes from Barry. The article is addressing the faint young sun problem and the climatic consequences for the early Earth of a reduced solar "constant". Without additional greenhouse gas in the atmosphere, the early Earth would have been an inhospitable snowball.

have you read Lovelock?

This work shows that the Earth system (including its biota) formed a temperature regulating system.

If we apply the same logic to Mars, as Lovelock did, we see at once that the planet is now dead to all intents and purposes - as regards the surface anyway. It is frozen to an average depth of 10 km. Lovelock was able to use Earth-bound telescopes to predict the Viking result, on a budget 99.99% smaller.

Early Mars had a colder surface (due to the faint young sun and the lack of stable high-pressure greenhouse atmosphere) and, except for the first few hundred million years, extra internal heat doesn't significantly reduce the melting depth.