Positive feedbacks in climate processes can obscure the initial drivers of climate phenomena. Some recent global climate model (GCM) studies partially circumvent this issue by controlling the wind stress felt by the surface ocean such that the atmosphere and ocean become mechanically decoupled. Most mechanical decoupling studies have chosen to override wind stress with an annual climatology. In this study we introduce an alternative method of interannually variable overriding which maintains higher frequency momentum forcing of the surface ocean. Using CESM1, we then compare the size of the residuals between these two methods of overriding with a freely evolving control integration. We find that the simple act of overriding with a climatology, as has been done in previous studies, creates sea surface temperature (SST) residuals throughout the global oceans on the order of $0.5-1^\circ$C. This is substantially larger than residuals from the interannually variable overriding case introduced here. We attribute the SST biases in the climatological overriding case to the lack of synoptic and subseasonal variability, which creates too shallow of a mixed layer throughout the global surface ocean. This shoaling of the mixed layer reduces the effective heat capacity of the surface ocean and prevents anomalous heat from mixing into the thermocline. These results have implications for the reevaluation of past studies which have used climatological wind stress overriding and for avoiding these biases in future wind stress overriding studies by using interannually varying wind stress fields.