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In particular, I'm interested in the heat contained in the stratosphere, mesophere, and thermosphere.

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    $\begingroup$ Can't be a lot. $\endgroup$ – gerrit Apr 16 '14 at 20:23
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    $\begingroup$ The two main hotspots are the thermosphere and stratosphere (near the o-zone layer), but these amounts are most likely minimal compared to the heat of total earth system. That said, the top of the stratosphere (warmest part) is still slightly below 0°C. atmospheric temperature profile $\endgroup$ – DrewP84 Apr 17 '14 at 22:43
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Mass at 21.9.1998 for Height 140 km -1000 km was $6.16\cdot10^{10} \mathrm{kg}$.
Avg. Temperature; $725 \mathrm{K}$

Roughly the mass is divided as follows;
$\mathrm{O}$, $\mathrm{O}_2$; $252 \cdot10^9 \mathrm{kg}$, “16” Molecule amount $N = 9.5\cdot10^{35}$,
Heat capacity; $920 \mathrm{J}/(\mathrm{kg} \mathrm{K})$

$\mathrm{N}$, $\mathrm{N}_2$; $364 \cdot10^9 \mathrm{kg}$; “14” Molecule amount $N = 1.56\cdot10^{36}$,
Heat capacity; $1040 \mathrm{J}/(\mathrm{kg}\mathrm{K})$

$\mathrm{He}$; $35.2\cdot10^6 \mathrm{kg}$, “4” Molecule amount $N = 5.3\cdot10^{33}$,
Heat capacity; $5193 \mathrm{J}/(\mathrm{kg} \mathrm{K})$

$\mathrm{H}$; $1.34\cdot10^6 \mathrm{kg}$, “1” Molecule amount $N = 0.8\cdot10^{33}$,
Heat capacity; $14304 \mathrm{J}/(\mathrm{kg}\mathrm{K})$

Total Heat capacity; $61.2\cdot10^{12} \mathrm{J}/\mathrm{K}$ Quelle; My own work.

From here you can calculate $725 \mathrm{K} \cdot 61.2 \cdot10^{12} \mathrm{J}/\mathrm{K} =44.4 \cdot10^{15} \mathrm{J}$

Please note that most of the heat is at the lower atmosphere plain because >99% of the mass is there.

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