Numerical experiments with a coupled model in which the ocean component is a GCM and therefore explicitly calculates the heat budget of the entire upper ocean support this suggestion. To accommodate an increase in the equatorial surface heating, the ENSO system sucks more heat into the equatorial upper ocean with a stronger zonal SST contrast during La Niña, and then pushes the heat poleward with a stronger El Niño warming.
In this "heat pump" picture for ENSO, El Niño acts as a regulator of the equatorial upper ocean heat content. Its existence and strength in the present climate owes not only to coupled wave dynamics, but also to the strong surface heating over the equatorial Pacific, and the high heat content the surface heating creates.
This "heat pump" picture sheds new light on the question of why there is no El Niño in the tropical Atlantic ocean. It also has important implications for the regulation of the tropical maximum SST, and for the response of ENSO to global warming.