The mechanics of ENSO are described in terms of the differing atmosphere - ocean feedbacks associated with El Niña and La Niño patterns. The logic seems plausible. However, much of the feedbacks involve exchanges between sensible heat and latent heat energy, which across the globe, do not result in total energy gains or losses.

May I suggest another mechanism that may also have considerable influence on global temperature? During a La Niño pattern, western Pacific waters flow south rather than flowing east along the Equator. The southward meridional flow brings warm and salty water toward the Ross Sea region. Salty water, combined with Antarctic chilling is the recipe for cold-water downwelling.

To the extent that ocean thermal content is reapportioned such that the volume of cold water (which cannot interact with air and space) is below the interactive surface and warmer waters remain at the interactive surface, Stefan-Boltzmann Law dictates that more heat energy will be emitted and Earth's surface will attain a new equilibrium at a cooler temperature.

A new perspective on El Niña might follow: the warming effect is due to the absence of a La Niño cooling effect. Simply shuffling a given volume of water with a total thermal content that varies (i.e., warm water and cold water) from one location to another does not change the total thermal content. 

The vertical reapportionment that increases the volume of deep cold and concentrates a thinner veneer of surface warmth in the world ocean is possibly the mechanism that brought about the Cenozoic Cooling and was the mechanism that repeatedly caused cooling during the latter parts of post-MPT interglacials. Global coolings occur when meridional circulation from low to high latitudes is enabled and polar conditions are right for downwelling.