What was the Earth's mean temperature 3,5 billion years ago (3,5 Bya ) ?
Lets see:
Sun's irradiating intensity was weaker.
It was only 75 % of the present,
S = 0,75*So
And Earth rotated twice as fast then,
1 rotation in 12 hours.
Lets calculate:
Earth’s Without-Atmosphere Surface Mean Temperature calculation Tmean.earth.3,5 Bya
So = 1.362 W/m² ( "So" is the present Solar constant )
Earth’s albedo: aearth = 0,30
Φearth = 0,47
β = 150 days*gr*oC/rotation*cal – is a Rotating Planet Surface Solar Irradiation INTERACTING-Emitting Universal Law constant
N = 2 rotations /per day, was Earth’s sidereal rotation spin at 3,5 Bya
cp.earth = 1 cal/gr*oC
σ = 5,67*10⁻⁸ W/m²K⁴, the Stefan-Boltzmann constant
Earth’s Without-Atmosphere Mean Surface Temperature Equation Tmean.earth is:
Tmean.earth = [ Φ (1-a) So (β*N*cp)¹∕ ⁴ /4σ ]¹∕ ⁴
Τmean.earth.3,5 Bya = [ 0,47(1-0,30)*0,75*1.362 W/m²(150 days*gr*oC/rotation*cal *2rotations/day*1 cal/gr*oC)¹∕ ⁴ /4*5,67*10⁻⁸ W/m²K⁴ ]¹∕ ⁴ =
Τmean.earth.3,5 Bya = [ 0,47(1-0,30)*0,75*1.362 W/m²(150*2*1)¹∕ ⁴ /4*5,67*10⁻⁸ W/m²K⁴ ]¹∕ ⁴ =
Τmean.earth.3.5 Bya = ( 6.167.274.722,0 )¹∕ ⁴ = 280,23 K
Tmean.earth.3.5 Bya = 280,23 Κ
or Tmean.earth.3,5 Bya = 7 oC.
Conclusion:
3,5 billion years ago planet Earth had a sustainable for life mean temperature of 7 oC.
From Wikipedia: " Among the earliest fossil evidence for life is microbial mat fossils found in 3.48 billion-year-old sandstone in Western Australia,[63]".