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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. Let's assume that the average specific heat of the earth's matter is that of silica (SO₂), ca. 0.7 J/g. 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
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Years of world energy supply from 1K            7.31E+06
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That's actually less than I thought, by a factor of 100 or 1000 or so, but still ... long.

_{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.}