How Hot Were the Oceans When Life First Evolved?

#1
http://www.astrobio.net/news-exclusive/h...t-evolved/

EXCERPT: We know little about Earth’s surface temperatures for the first 4 billion years or so of its history. This presents a limitation into research of life’s origins on Earth and also how it might arise on distant worlds as well. Now researchers suggest that by resurrecting ancient enzymes they could estimate the temperatures in which these organisms likely evolved billions of years ago. The scientists recently published their findings in the journal, Proceedings of the National Academy of Sciences. [...] Their research suggests that Earth’s surface cooled from roughly 167º F (75º C) about 3 billion years ago to roughly 95º (35º F) about 420 million years ago. These findings are consistent with previous geological and enzyme-based results. Garcia said such a dramatic cooling is hard to fathom, emphasizing how scientists need to remember how different conditions were in the past when figuring out how life evolved over time....
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#2
I'd speculate that there are several sources of ancient heat. One is from the Earth itself, from residual heat due to its violent formation and from heavy asteroid bombardment in its early days. Radioisotope decay might contribute. So the Earth's own heat can probably be assumed to have been higher just a few hundred million years into Earths history (when life presumably appeared) than it is now, 4.5 billion years later.

But... the Sun was supposedly less energetic in those days. So solar heating from the Sun was arguably less.

I've seen speculations that the early Earth was everything from molten to a frozen snowball. I'd like better information on this, since I'm very interested in the origin of life.

An additional wildcard is the kind of dramatic migrations that planets are now imagined to have undergone in their formation years. So, was the Earth always in the orbit that it's in now or was it once closer or further from the Sun? Or did that early migration stuff all take place much earlier than the appearance of liquid water and life on Earth, back when the Sun was still surrounded by a planetary accretion disk?
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