Unfortunately, internal heat is irrelevant for global surface temperature.

For the modern Earth, sunlight gives 1350 W/m^2. Geothermal energy gives ~80 milliWatts/m^2 - a ratio of over 15,000:1

Even if you boost geothermal energy by a factor of 10 (plausible) or 100 (wildly implausible) for the early Earth, and reduce sunshine to the 70% of the "Faint Young Sun", internal energy is still less than 1% of sunshine.

We need to think more carefully about what the early Earth was like, and where photosynthesis took place, and what fraction of the planet was ice covered through time.

The NeoProterozoic "Snowball Earth" models are in interesting example of non-steady states of the biosphere. Other models of the Archean might need to be similarly inventive, rather than boring steady-state systems.