Reference: Daniel V. Schroeder, An Introduction to Thermal Physics, (Addison-Wesley, 2000) – Problem 1.61.
The temperature of the Earth increases as we go further underground so, given that the rock that makes up the Earth’s crust has a thermal conductivity and there is a temperature difference between a point underground and the Earth’s surface, the Earth is actually losing energy by heat conduction. Using the values given by Schroeder, we have and . The rate of heat conduction in an area of is therefore
Although the rate of heat loss is quite small for a square metre, if we assume this value applies over the entire Earth (radius 6400 km), the total heat loss is
Although this sounds like a lot, to put it in perspective, the sun’s luminosity is , and the peak energy received on Earth from the Sun is around , which is around 27,000 times the rate at which the geothermal energy is being lost.