It has recently been suggested that observations of neutral density from satellite accelerometer data indicate a strong cooling occurred in the upper thermosphere during the January 2009 sudden stratospheric warming (SSW). The 2009 warming was a major event with winter polar stratospheric temperatures increasing by 70 K. This January period has been re-examined with three independent models: the NRLMSISE-00 empirical model; the physics-based coupled thermosphere, ionosphere, plasmasphere, electrodynamics model (CTIPe); and the whole atmosphere model (WAM). The analysis of this period and comparison with the neutral density observations reveals that there is, in fact, no evidence at any latitude for a large-scale or global decrease in upper thermosphere density or temperature in response to the SSW. The observed decrease in density and temperature can be amply accounted for by small changes in geomagnetic activity during this period. On the contrary, the WAM numerical simulations of the period suggest a possible small globally averaged upper thermosphere warming and neutral density increase by 5% during the SSW. This warming would have been difficult to discern in the local-time sampling of the CHAMP observations due to likely change in the diurnal density variation during the SSW, and due to a much larger contribution to the variability from geomagnetic sources. At this stage, therefore, it is not possible to ascertain if a cooling or warming occurred in the upper thermosphere in response to the stratospheric warming.