Assume an underground city existed below the surface of Antarctica. The ice sheet is ~2 miles thick on average. At what range/depth would the earth's thermal heat allow livable temperature for humans, assuming the civilization is technologically medieval (so no modern heating/cooling systems). Note: "Livable" does not mean comfortable. Extreme hot or cold would be fine as long as humans can reasonably survive in it.
Please ignore the obvious issues with an underground city (such as lighting, respiration, excavation, food sources, etc) and focus solely on the temperature aspect.
I assume there would be little subterranean temperature change between the polar day and night (despite each being six-months long).