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The double-peaked response of the tropical stratospheric temperature profile to the 11-year solar cycle (SC) has been well documented. However, there are concerns about the origin of the lower peak due to potential aliasing with volcanic eruptions or the El Nino Southern Oscillation (ENSO) detected using multiple linear regression (MLR) analysis. We confirm the aliasing using the results of the chemistry-climate model (CCM) SOCOLv3 obtained in the framework of the IGAC/SPAR Chemistry-Climate Model Initiative phase 1 (CCMI-1). We further show that, even without major volcanic eruptions included in transient simulations, the lower stratospheric response exhibits a residual peak when historical sea surface temperatures (SST)/sea ice coverage (SIC) are used. Only the use of climatological SSTs/SICs in addition to background stratospheric aerosols removes volcanic and ENSO signals and results in an almost complete disappearance of the modeled solar signal in the lower stratospheric temperature. We demonstrate that the choice of temporal sub-period considered for the regression analysis has a large impact on the estimated profile signal in the lower stratosphere: at least 45 consecutive years are needed to avoid the large aliasing effect of SC maxima with volcanic eruptions in 1982 and 1991 in historical simulations, reanalyses and observations. The application of volcanic forcing compiled for phase 6 of the Coupled Model Intercomparison Project (CMIP6) in the CCM SOCOLv3 reduces the warming overestimation in the tropical lower stratosphere and the volcanic aliasing of the temperature response to the SC, although it does not eliminate it completely.