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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 Kardashev Type III civilization, provided we manage to survive all the bottlenecks ahead. As Ray Kurzweil remarked 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.) If we assume an increase of 2% per year, Wolfram Alpha plots this nice curve which shows when the supply needed in a single year would amount to the Earth's thermal energy corresponding to a 1K difference. Aparently that point would be reached in 800 years, not 7 million. Note how the curve doesn't make a dent until year 500 or so.⁴

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 Kardashev Type III civilization, provided we manage to survive all the bottlenecks ahead. As Ray Kurzweil remarked 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.) If we assume an increase of 2% per year, Wolfram Alpha plots this nice curve which shows when the supply needed in a single year would amount to the Earth's thermal energy corresponding to a 1K difference. Apparently that point would be reached in 800 years, not 7 million. Note how the curve doesn't make a dent until year 500 or so.⁴

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 Kardashev Type III civilization, provided we manage to survive all the bottlenecks ahead. As Ray Kurzweil remarked 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.)

_{³ Obligatory (but somewhat depressing) xkcd.}

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 Kardashev Type III civilization, provided we manage to survive all the bottlenecks ahead. As Ray Kurzweil remarked 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.) If we assume an increase of 2% per year, Wolfram Alpha plots this nice curve which shows when the supply needed in a single year would amount to the Earth's thermal energy corresponding to a 1K difference. Aparently that point would be reached in 800 years, not 7 million. Note how the curve doesn't make a dent until year 500 or so.⁴

_{³ Obligatory (but somewhat depressing) xkcd.}

_{⁴ A similar curve (with a time interval of perhaps 150 years instead of 800) could be drawn for the consumption of mineral oil. In the mid-1800s anybody predicting that one day not too far into the future we'll worry about using up all of the easily accessible mineral oil of the Earth would have been laughed out of town.}

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.³

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 (SO₂), ca. 0.7 J/(g*K). This leads to the following results:¹

Specific heat of silica (J/(kg*K))              7.00E+2
Earth's mass (kg)                               5.97E+24(2)
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 ΔT=1K         7.31E+06
========================================================

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 civilization, provided we manage to survive all the bottlenecks ahead. As Ray Kurzweil remarked 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.)

_{¹ The original primary energy consumption number is from the IAEA. Mtoe stands for mega ton oil equivalent, roughly 4,187e+10 J.}

_{⁽²⁾ Give or take 10^20}

_{³ Obligatory (but somewhat depressing) xkcd.}

_{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.}

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.³

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 (SO₂), ca. 0.7 J/(g*K). This leads to the following results:¹

Specific heat of silica (J/(kg*K))              7.00E+2
Earth's mass (kg)                               5.97E+24(2)
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 ΔT=1K         7.31E+06
========================================================

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 Kardashev Type III civilization, provided we manage to survive all the bottlenecks ahead. As Ray Kurzweil remarked 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.)

_{¹ The original primary energy consumption number is from the IAEA. Mtoe stands for mega ton oil equivalent, roughly 4,187e+10 J.}

_{⁽²⁾ Give or take 10^20}

_{³ Obligatory (but somewhat depressing) xkcd.}

_{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.}