<< 
Tom, I believe, is correct that the earth's surface was once
very hot (molten), then less hot (100C), then even less hot
still.  However, he may be overestimating how long it took
to cool.  It can go from molten to 100C in 100My and from
100C to 0C in another 100My even while being periodically
reheated locally by impacts.  0.1Gy is a LONG time.

Tom does have a good question as to how Mars could be
warm enough to have liquid water if Earth was a snowball.
My guess:  Mars had liquid water only episodically and
locally.  After a comet impact or a volcanic eruption, there
was some water locally for a few thousand years or so,
but then everything froze over again, and the water either
escaped to space or was adsorbed by the soil.

 >>


IF the heat wasn't local but throughout the solar system, then Tyler raised an
interesting point in an earlier post.
Liquid water would first be on the cooler Mars - while Earth would still be
water vapor.

That suggests that IF there is a specific temperature cycle, a specific temp
window of opportunity  for life to begin (and  we know its at least liquid
water range 0-100C, though I think it may well be a more narrow range of  25
degree  near the top of the 0-100C temp range , say 73-98C for ex.)
then mars may have had the first chance for life to form.

We may be a 2nd attempt even in our own solar system.

Tom
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