We generally tend to underestimate sizes and masses of celestial bodies. A little giveaway is that for all non-astronomical means and purposes we consider the Earth's mass *infinite* without any measurable error.<sup>3</sup>

Let's make an estimation: How does the heat stored in the planet Earth relate to humanity's energy production? I'm only interested in an order of magnitude here. 
Let's assume that the average specific heat of the earth's matter is that of silica (SO<sub>2</sub>), ca. 0.7 J/(g*K). This leads to the following results:<sup>1</sup>

<pre>Specific heat of silica (J/(kg*K))              7.00E+2
Earth's mass (kg)                               5.97E+24<sup>(2)</sup>
Earth's energy/K, assuming it's all silica      4.18E+27
	
World primary energy supply 2015 (Mtoe)         1.36E+4
J/Mtoe	                                        4.19E+16
World primary energy supply 2015 (J)	        5.60E+20
--------------------------------------------------------
Years of world energy supply from &Delta;T=1K         7.31E+06
========================================================</pre>

That's actually less than I thought, by a factor of 100 or so, but still ... long. It's noteworthy though that this estimate assumes a constant energy supply for the next couple million years. That is rather unlikely since we'll be on our way to a [Kardahev Type III](https://en.wikipedia.org/wiki/Kardashev_scale) civilization, provided we manage to survive all the bottlenecks ahead. As [Ray Kurzweil remarked](https://www.kurzweilai.net/the-law-of-accelerating-returns) we tend to underestimate exponential growth because we are hardwired for linear relations. A civilization with exponentially growing resource usage (like our current one) will not be able to rely on geothermal energy for geological time frames. (It will not be able to rely on solar energy either, if we extend the time frame just a bit.)


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<sub><sup>1</sup> The original primary energy consumption number is from [the IAEA](https://www.iea.org/publications/freepublications/publication/KeyWorld2017.pdf). *Mtoe* stands for *mega ton oil equivalent*, roughly 4,187e+10 J.</sub>

<sub><sup>(2)</sup> Give or take 10^20</sub>

<sub><sup>3</sup> Obligatory (but somewhat depressing) [xkcd.](https://what-if.xkcd.com/8/)</sub>

<sub>It's entirely possible that I made a mistake and the result is off by a few decimal digits (although it's probably not too small); I appreciate corrections.</sub>