To investigate the role of ENSO in regulating the time-mean thermal stratification of the equatorial Pacific, perturbation experiments are conducted in pairs with a coupled model. In one experiment, ENSO is turned off while in the other experiment ENSO is kept on. Perturbations are introduced through either enhancing tropical heating or increasing subtropical cooling. In the absence of ENSO, the time-mean difference between the warm-pool SST (Tw) and the characteristic temperature of the equatorial thermocline (Tc) responds sensitively to either enhanced tropical heating or enhanced subtropical cooling. In the presence of ENSO, such a sensitivity to destabilizing forcing disappears. The lack of sensitivity in the response of Tw-Tc is linked to a stronger ENSO in response to the destabilizing forcing. ENSO in the model acts as a basin-scale heat "mixer" that enables surface heat to be transported to the depths of the equatorial thermocline. The study raises the question whether models with poor simulations of ENSO can give reliable predictions of the response of the time-mean climate to global warming.