To predict the future climate on multiyear timescales, it is crucial to understand how the changing external radiative forcing (CO2 and Ozone) drives the climate and impacts the skill of intra-seasonal to multiyear climate prediction. In this study, we use a 1-degree configuration of the GEOS-MITgcm coupled general circulation model to understand the response to different levels of observed external forcing from past decades. We ran `perpetual' experiments for 1992, 2000, and 2020, each with their respective year’s external forcing. Results of the perpetual simulations showed that the Northern Hemisphere polar stratospheric temperature increases from 1992 to 2000, whereas it decreases from 2000 to 2020. We further conducted a 10-member ensemble of transient climate simulations for the 1992--2020 period with observed external forcing and found a similar positive temperature trend from 1992 to 2000 and a negative trend from 2000 to 2020. This is in contrast to the general expectation that the stratosphere cools as CO2 increases. A similar opposing pattern of temperature trends exists in reanalyses and CMIP6 historical simulations with a well-resolved stratosphere. Analysis of the results showed that the external forcing change during the years 1992-2000 increases the tropical diabatic heating, and intensifies the wave activity related meridional heat transport to the Northern Hemisphere mid to high-latitudes, which, in turn, increases the polar stratospheric temperature. In contrast, during the 2000-2020 period the meridional heat transport decreases, contributing to a decrease in the polar stratospheric temperature. The long-wave radiation change in these periods responds to the changing temperature and so doesn't play a significant role in driving them.