Multidecadal sea surface temperature covariance in the southern Atlantic and Indian Oceans within the 20°–45°S band (termed the SAIOs) has been detected, but the origins of these variations remain uncertain. This study focuses on the decade‐long warming surge (0.43°C/decade) during 1965–1975 and the stalled warming pace (0.05°C/decade) thereafter. Observations and models overall suggest the essence of external forcing in controlling the warming rates of these two periods. Specifically, the 1963 eruption of Mount Agung caused an abrupt cooling of the SAIO, and the recovery of radiative heating during the following decade led to rapid surface warming. The persistent positive trend of the Southern Annular Mode since the late‐1970s has retarded the SAIO warming, primarily by enhancing surface wind speed and latent heat release. Although internal variability can also affect the SAIO through atmospheric teleconnections, its role is overall secondary during the two periods. Plain Language Summary: Sea surface temperatures (SSTs) in the southern Atlantic and Indian Oceans (SAIOs) show prominent decade‐to‐decade variations, with notable impacts on global and regional climates. However, the origins of these multidecadal variations are largely unknown. While previous studies overall stressed internal climate variability, this study suggests essential effects of external drivers on the rapid warming of 1965–1975 and the subsequent slowdown. Specifically, atmospheric aerosols from the 1963 eruption of Mount Agung caused an abrupt drop in surface solar radiation, and the recovery of solar heating in the following decade led to accelerated surface warming in the SAIO. Since the late 1970s, the human‐induced Antarctic ozone hole drove a positive trend in the Southern Annular Mode. This trend enhanced the surface winds over the SAIO and attenuated the SST warming. In addition, impacts from internal variability, such as the Interdecadal Pacific Variability, are also considerable during the two periods. Key Points: The sea surface temperature (SST) warming rate of the southern Atlantic and Indian Ocean (SAIO) shows multidecadal variations, with a short‐term surge during 1965–1975 and decelerated warming thereafterThe 1963 eruption caused a dip in the SAIO SST, and the subsequent dissipation of volcanic aerosols led to accelerated warming of 1965–1975The Interdecadal Pacific Variability and Southern Annular Mode also modulate the warming rate of the SAIO through their signatures in atmospheric circulation [ABSTRACT FROM AUTHOR]