Without the sun to keep the Earth's temperature topped up to something comfortable, what would be the equilibrium surface temperature range. It would obviously be a balance between outgoing radiation and geothermal conduction to the surface. This question is prompted by Anixx's recent question on planetary cooling time without the sun.
Assuming a thermodynamic equilibrium between heat from below and heat escaping into outer space, and assuming an energy from below of 44 to 47 terawatts (the Earth's current internal heat budget), that means the surface temperature would be about 35 or 36 kelvins by the Stefan-Boltzmann law: $$\varepsilon \sigma A T^4 = \phi$$ where $\varepsilon$ is the surface's emissivity in the thermal range (which I assumed to be one), $\sigma$ is the Stefan-Boltzmann constant (5.670367×10-8 W/M2/K4 in SI units) , $A$ is the Earth's surface area, $T$ is the surface temperature, and $\phi$ is the energy supplied to the Earth's surface from below.
Note that atmospheric effects are a non-concern for this very low temperature. The Earth would have no atmosphere except perhaps some trace helium and hydrogen gas.