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 of HALOE T(p) values for 1993–2005 are for six levels from 2.0 to 0.3 hPa with a vertical resolution of about 4 km and for eight latitude zones from 65°S to 65°N. The analyses account for the forcing effects from the 11‐yr solar cycle. 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. Near‐global T(p) trends are of order −0.5 K/decade but have a minimum of −0.2 K/decade at 1.0 hPa; they are clearly negative in the southern but slightly positive in the northern hemisphere. The combined radiative forcings from CO2, H2O, and ozone vary between −0.4 and −0.7 K/decade for 1993–2005 and are hemispherically symmetric. The 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 at low latitudes for the tracer, methane (CH4), increase from 2% to 4%/decade from 50 to 10 hPa and then to ~6%/decade by 5 hPa. Analyses of time series of CH4 across the stratopause reveal subseasonal scale variability within the northern hemisphere that reduces the significance of the T(p) trends.