In climate simulations from Phase 3 and Phase 5 of the Coupled Model Intercomparison Project (CMIP), the multimodel mean tropical tropospheric temperature (TTT) warms roughly two times more than satellite observations since 1979. It has been suggested that this longstanding difference is attributable to model climate sensitivity biases. Using the latest CMIP6 simulations, we find that the multimodel average trend is still 1.5 to 3.2 times larger than satellite-derived TTT trends. We note, however, that model realizations performed with a single model exhibit widely varying TTT trends over this 40-year period. A subset of realizations from models with both small and large climate sensitivity are in accord with satellite-derived warming trends, indicating that internal variability, in addition to model climate sensitivity, is a key consideration when comparing modeled and observed warming over the satellite era. In the CESM large ensemble, model realizations with relatively small TTT trends are accompanied by subdued sea surface temperature (SST) change in the tropical central and eastern Pacific and enhanced warming in the western equatorial Pacific at a depth of 150 m. Observations and reanalysis of ocean temperature change show a similar pattern, suggesting that the observed TTT trend has been reduced by natural climate variability. Our results indicate that internal climate variability is sufficiently large to explain TTT trend differences between models and satellite observations.