[1] We characterize middle-atmosphere polar warming (PW) using nearly three Martian years of temperature observations by the Mars Climate Sounder. We report the observed structure of PW and share hypotheses as to possible explanations, which have yet to be tested with global dynamical models. In the data, PW manifested between p = 15 Pa and p(-)4.8 x 10(-3) Pa. The latitude where PW maximized shifted poleward with decreasing pressure. The nightside magnitude was larger than the dayside magnitude. The maximum nightside magnitudes ranged from 22 to 67 K. As expected, the annual maximum magnitude in the north occurred during late-local fall to middle-local winter. In the south it occurred during late-local winter. Also as expected, the maximum magnitude near MY 28' s southern winter solstice was smaller than that at that same year's northern winter solstice, when a global dust storm was occurring. Unexpectedly, the maximum magnitude at southern winter solstice was comparable to that at northern winter solstice for both MY 29 and MY 30, years that did not experience global dust storms but certainly experienced greater dust loading during L-s = 270 degrees than L-s= 90 degrees Another unexpected result was a hemispheric asymmetry in PW magnitude during most of the observed equinoxes. This paper also provides tables of (1) averaged temperatures as a function of latitude, pressure, and season, and (2) the maximum polar warming features as a function of pressure and season. These tables can be used to validate GCM calculations of middle-atmosphere temperatures and constrain calculations of unobserved winds. Citation: McDunn T., S. Bougher, J. Murphy, A. Kleinbohl, F. Forget, and M. Smith (2013), Characterization of middle-atmosphere polar warming at Mars, J. Geophys. Res. Planets, 118, 161-178, doi: 10.1002/jgre.20016.