This study considers time series of temperature versus pressure, T(p), from the Halogen Occultation Experiment (HALOE) across the stratopause region, where the effects of radiative forcings from the greenhouse gases (CO2 and H2O) and from ozone are most pronounced. Trend analyses are from 1993-2005 for HALOE T(p) values at seven levels from 3.0 to 0.3 hPa with a vertical resolution of about 4 km and for eight latitude zones from 65°S to 65°N. The HALOE trends at 2.0 hPa are of the order of -1.0 K/decade across the tropics and subtropics, but then become smaller (-0.5 K/decade) at the middle latitudes. The near-global HALOE trend profile has a minimum cooling rate of -0.2 K/decade at 1.0 hPa, although it is more negative in the southern hemisphere and slightly positive in the northern hemisphere. The combined radiative forcings from CO2, H2O, and ozone are from -0.4 to -0.6 K/decade for 1993-2005 and are hemispherically symmetric. HALOE temperature trend and total radiative cooling profiles differ from those reported from observations and calculations for 1980-2000, mainly because the ozone trends changed from clearly negative in the 1980s through mid-1990s to slightly positive during the time of HALOE. Trends for the tracer, HALOE methane (CH4), increase from 2 to 4 %/decade from 50 hPa to 10 hPa, indicating an acceleration of the Brewer/Dobson circulation. Analyses of time series of CH4 across the stratopause reveal more variability in the northern hemisphere, where wave dissipation likely contributes to the heating.