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I have tried without luck to find a graph of temperature change through the atmosphere that goes further up than about 100 km. On this graph:

http://www.windows2universe.org/kids_space/profile.jpg
(Source: http://www.windows2universe.org/kids_space/temp_profile.html)

as on many others the temperature rises and rises and continues like that out of the scale. How will the temperature curve look further up when the exosphere gets closer (at about 700 km or so, according to Wikipedia)? What is the max temperature the thermosphere will reach?

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    $\begingroup$ I doubt that the atmosphere above 100km is in thermal equilibrium. Did you check that assumption? If it is not, then there is not one temperature, but one may have to look at multiple species of molecules, atoms, plus ions and electrons and maybe even talk about the actual velocity distribution of these species rather than a single temperature profile. $\endgroup$
    – CuriousOne
    Commented Dec 13, 2014 at 15:15
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    $\begingroup$ At least, above 100 km altitude, it's over the Kármán limite considered as the limit between space and atmosphere. $\endgroup$
    – Babounet
    Commented Dec 13, 2014 at 15:17
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    $\begingroup$ You may want to take a look at this: eiscat3d.se/drupal/sites/default/files/IISRWS2011/…. The graphs show pretty nicely why it's not a good idea to treat the atmosphere above 100km as a homogeneous gas with a well defined temperature. $\endgroup$
    – CuriousOne
    Commented Dec 13, 2014 at 15:43

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A team at the University of Western Ontario used a lidar to measure "temperature" by inferring it from the blackbody spectrum of atmospheric gases at various heights. They arrived at this: enter image description here

However, as noted in the comments to the OP, the atmosphere at very high altitudes isn't really in thermal equilibrium and doesn't have a well-defined concept of temperature.

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