"Evolutionary models of the solar interior lead to the prediction that the Sun should have been about 25% fainter 3.8 Gyr ago (Gough, 1981; Bahcall et al., 2001). This is a fairly robust result that has been known for a long time. However, this creates significant difficulties for those who study the climate history of planets in our solar system. With the young Sun this faint, the planets should have been significantly colder than they are now. On Earth and Mars, surface water should have been frozen, but this contradicts geologic evidence that abundant water existed and flowed on the surfaces of both of these planets. This is the so-called “Faint Young Sun” paradox (Sagan and Mullen, 1972; Kasting, 1991). Most attempts to solve this problem have appealed to increased amounts of greenhouse gases in the early atmospheres of Earth and Mars, which allowed the surface temperatures to remain similar to present-day temperatures despite a fainter Sun (see Walker, 1985; Kasting and Ackerman, 1986; Kasting, 1991)."
http://solarphysics.livingreviews.org/Articles/lrsp-2004-2/articlesu9.html

I got idea.
If we were in a deep ice age, we could travel down a couple miles under the earth's surface and be quite warm. Today the earth's suface on land is 30-50 km thick and under ocean the crust is thinner around 10 km thick. What if 3-4 billion years ago the Earth crust was significantly thinner?
Now, there is two differnent aspects about this. First is the relatively short period since the earth was a molten ball of lava- created by very large impactors [including the Moon]. So I get the part about the surface cooling fairly rapidly in terms of geologic time, but would cool to our current crust thickness within a relatively short time geologically?
For instance it's thought that perhaps Mars currently has a thick crust, but 3 billion years ago mars was thought to be more geologically active and I assume the thinking is that the crust was not as thick as it is today.
What would Mars look like today if it had a thin crust, say 5-10 km thick? And we also think that in Earth's early history, Earth was more volcanic active. If Earth is more volcanic active wouldn't indicate a thinner crust- wouldn't a thinner crust result in the earth being more volcanic active. Now if Earth's crust was on average 1/2 it's current thickness less for first couple billion years, wouldn't that result in significantly more heating to the atmosphere then it does currently?
The other aspect is that thicker continential crust could an accumulating process due to volcanic activity, could it not be possible that we had far less continential crust 3 billion years ago, instead of 30% of the suface being land could there have been 5% or less. Could be there is reason that the biggest ocean in the world, the pacific, is ringed by volcanos.
There are also other factors, the Moon was closer and giving more tidal energy. If the Earth reason for being hot is because of radioactive material in the core, wouldn't after billions of years the Earth have less radioactivate material in it's core.

So maybe more heat was coming from the ground: more tidal, thinner crust, more radioactive core. And world is different super volcano creating vast lakes of lava. Hawaii was built from a hot spot, think of a super volcano in process building a far bigger island. Earth isn't blue marble from space, it's Mordor. All this volcanic dust would block some of the sunlight from entering , but it's greenhouse affect in reverse. Greenhouse gases block infrared radiation and you various lakes lava around world in which it's heat is being blocked from escaping into space.