MATH

Fi = solar power flux incident on planet Earth;
Fr = solar power flux reflected off planet Earth;
A = (Fr / Fi) = Planetary albedo A;
(Fi – Fr) = Fi (1 – A) = solar power flux absorbed by planet Earth;

Planck showed that emitted thermal radiation power = K T^4

where:
T = the absolute temperature in degrees kelvin
K is a factor that is nearly constant but that for planet Earth is slightly dependent on the atmospheric greenhouse gas concentrations.

Over thousands of years the surface temperature of planet Earth has become nearly constant with time implying that to a good approximation:
absorbed power = emitted power
or
Fi (1 – A) = K T^4

Injection of CO2 into the atmosphere reduces K. If Fi and A are both constant,
as K decreases, T increases.

Albedo A is proportional to the fraction of Earth's surface covered by highly reflective snow and ice. As A decreases due to ice melting, temperature T increases.

As Earth warms A will decrease from about 0.30 to about 0.10. Thus:
[Fi (1 - 0.30)] / [Fi (1 - 0.10)] = K (T1)^4 / K (T2)^4
or
(0.7 / 0.9) = (T1 / T2)^4
or
T2 / T1 = (0.9 / 0.7)^0.25
or
T2 - T1 = T1 [(0.9 / 0.7)^0.25 - 1]
= T1 [0.06484]

For T1 = 270 degreees K: (T2 - T1) = 17.508 degrees C

The parameters K and A are presently both decreasing. If we fail to stop this decrease the corresponding rise in Earth surface temperature will doom all large land animals and many marine species.

This thermal runaway warming process should stop when all of Earth's surface ice has melted. At that time the albedo A will have decreased from about 0.30 to about 0.10 and the corresponding average Earth surface temperature T will have increased by about 17.5 degrees C.

About 56 million years ago, during a period known as the PETM (Paleocene-Eocene Thermal Maximum) the isotope record shows that all the ice melted.

Absent mankind's injection of fossil CO2 into the atmosphere the parameters A and K have a natural low level oscillation causing periodic glaciation driven by the passing proximity of other planets.