The UARS HALOE experiment has provided nearly 12 years (1991-2003) of retrieved temperature versus pressure profiles T(p) from about 5 hPa to just above 0.01 hPa. By applying multiple linear regression (MLR) analysis techniques to its zonally-averaged, temperature time series at specific pressure levels and latitudes, we are finding significant interannual (IA) and solar cycle (SC) terms in the presence of larger-amplitude, seasonal cycle terms. In addition, we note that the search for a cooling trend depends critically on a proper accounting for the weaker amplitude IA and SC terms. After these weaker terms have been considered, we have occasionally found a significant cooling trend of about 0.9 to 1.4 K per decade in the low to middle mesosphere-most notably at 20S latitude.