We examine multiple factors in the representation of satellite-retrieved atmospheric temperature diagnostics in historical simulations of climate change during the satellite era (specifically 1979-2021) using GISS ModelE contributions to the Coupled Model Intercomparison Project (Phase 6) (CMIP6). The tropospheric and stratospheric trends in these diagnostics are affected by greenhouse gases (notably carbon dioxide and ozone), coupling with the ocean, volcanic aerosols, solar activity and compositional and dynamic feedbacks. We explore the impacts of internal variability, changing forcing specifications, composition interactivity, the quality of the stratospheric circulation, vertical resolution, and possible impacts of the mis-specification of volcanic aerosol optical depths. Overall trends and patterns over the satellite period are well captured, but discrepancies at all levels exist and have multiple distinct causes. We find that stratospheric comparisons (using Stratospheric Sounding Unit (SSU) retrievals and successor instruments) are most affected by variations in the representation of ozone depletion and feedbacks, followed by the volcanic signals. Tropospheric skill (using the Microwave Sounding Unit (MSU) retrievals) is affected by the trends in ocean temperature and tropospheric aerosols, but also by the representation of stratospheric processes through the impact of the Brewer-Dobson circulation on the height of the tropical tropopause. We do not find evidence of a systematic problem in the model climate sensitivity.