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Climate models struggle to produce sea surface temperature (SST) gradient trends in the tropical Pacific comparable to those seen recently in nature. Here, we find that the magnitude of the cloud‐SST feedback in the subtropical Southeast Pacific is correlated across models with the magnitude of Eastern Pacific multi‐decadal SST variability. A heat‐budget analysis reveals coupling between cloud‐radiative effects, circulation, and SST gradients in driving multi‐decadal variability in the Eastern Pacific. Using this relationship and observed feedback estimates, we find that internal Eastern Pacific SST variability is underestimated in most models. Adjusting for model bias increases the likelihood of generating a cooling trend at least as large as observations in preindustrial control simulations by ∼ ${\sim} $56% on average. If models underestimate climate "noise," as our results suggest, this bias should be accounted for when attributing the relative importance of forced versus unforced changes in the climate. Plain Language Summary: In recent decades, observed sea surface temperatures (SSTs) have cooled in the eastern tropical Pacific and warmed in the western tropical Pacific. Historical simulations using state‐of‐the‐art climate models fail to reproduce this pattern. We find that the feedback between low‐lying clouds and SSTs is related to the magnitude of naturally occurring SST variability in the Southeast Pacific. On average, climate models that have too weak a cloud‐SST feedback in the Southeast Pacific underestimate the likelihood of multi‐decadal cooling in the eastern Pacific in preindustrial simulations. Our results suggest that biases in cloud feedbacks may be causing models to underestimate internal SST variability. Key Points: Multi‐decadal Southeast Pacific sea surface temperature trends are related to the strength of the subtropical cloud feedbackCloud radiative effects amplify multi‐decadal Pacific sea surface temperature trends by impacting circulation and surface energy fluxesCorrecting model biases in cloud feedback raises the likelihood of internally producing Southeast Pacific cooling as large as observations [ABSTRACT FROM AUTHOR]