Thermosphere Climate Indexes (TCI) represent the 60-day running average of the global infrared cooling power radiated from the thermosphere by nitric oxide and by carbon dioxide. The TCI are accurately expressed as linear combinations of the 60-day running averages of the F10.7, Ap, and Dst indexes, thus providing terrestrial context to the long record of solar and geomagnetic indexes. We examine the percentile distribution in quintiles of the TCI generated using solar and geomagnetic indexes covering five complete solar cycles. We further assign adjectival descriptors (Cold, Cool, Neutral, Warm, or Hot) to these quintiles as the TCI largely indicate the global thermal state of the thermosphere. We suggest that the TCI are valuable new solar-terrestrial indexes due to the information they contain about the global thermosphere and due to their ease of calculation from standard indexes. Specifically, given dynamic range of the TCI associated with NO cooling, and its significant dependence on both solar irradiance and geomagnetic processes, we recommend that it be included henceforth as a new, standard solar-terrestrial Index. The NO TCI data show that the thermosphere was “Warm” only for a brief period of time at the maximum of solar cycle 24 and thus experienced the coolest solar maximum of the past seven solar cycles. As of February, 2018, the thermosphere power is in the lowest quintile of values, to which we assign the level of ‘Cold.’