Temperature versus pressure or T(p) time series from the Halogen Occultation Experiment (HALOE) have been generated and analyzed for the period of 1991--2004 and for the mesosphere and upper stratosphere for latitude zones from 40N to 40S. Multiple linear regression (MLR) techniques were used for the analysis of the seasonal and the significant interannual and solar cycle (or decadal-scale) terms. An 11-yr solar cycle (SC) term of amplitude 0.5 to 1.7 K was found for the middle to upper mesosphere; its phase was determined by a Fourier fit to the de-seasonalized residual. This SC term is largest and has a lag of several years for northern hemisphere middle latitudes of the middle mesosphere, perhaps due to the interfering effects of wintertime wave dissipation. The SC response from the MLR models is weaker but essentially in-phase at low latitudes and in the southern hemisphere. An in-phase SC response term is also significant near the tropical stratopause with an amplitude of about 0.4 to 0.6 K, which is somewhat less than predicted from models. Both sub-biennial (688-dy) and QBO (800-dy) terms are resolved for the mid to upper stratosphere along with a decadal-scale term that is presumed to have a 13.5-yr period due to their predicted modulation. This decadal-scale term is out-of-phase with the SC during 1991--2004. However, the true nature and source of this term is still uncertain, especially at 5 hPa. Significant linear cooling trends ranging from -0.3 K to -1.1 K per decade were found in the tropical upper stratosphere and subtropical mesosphere. Trends have not emerged so far for the tropical mesosphere, so it is concluded that the cooling rates that have been resolved for the subtropics are likely upper limits. As HALOE-like measurements continue and their time series lengthen, it is anticipated that better accuracy can be achieved for these interannual, SC, and trend terms.