The quasi-decadal oscillation (QDO) in the Earth's climate system fluctuated in phase with the 11-year period signal in solar total irradiance (STI) variability throughout the 20th century. The QDO was associated with global average upper ocean temperature variability dominated by the tropical global average from 20¿S to 20¿N. Earlier diagnosis of the tropical global average oceanic thermal budget found the anomalous warming tendency driven not by the radiative forcing (~0.15 W m-2) from the 11-year period signal in STI but by the larger anomalous quasi-decadal sensible plus latent heat flux (~0.5 W m-2) from the overlying troposphere. Now we diagnose the corresponding thermal budget of the tropical global average atmospheric temperature variability, finding it largest in the lower stratosphere (~0.8¿K), decreasing downward into the lower troposphere (~0.15¿K) and the upper ocean (~0.05¿K). These diagnostics find quasi-decadal temperature variability in the tropical lower stratosphere arising from a thermal balance between anomalous radiative forcing (1.0--1.5 W m-2) by ozone absorption of the 11-year signal in solar UV irradiance variability (modified by absorption of mean solar IR irradiance by volcanic aerosol variability) and variable longwave radiation and vertical advection. The latter two processes altered the vertical gradient of equivalent potential temperature in the tropical troposphere that allowed mean vertical circulation to drive an anomalous warming tendency in the lower troposphere. The latter matched the amplitude and phase of the downward quasi-decadal sensible plus latent heat flux anomaly that drove the anomalous warming tendency in the tropical global ocean.