Identifying the primary drivers of North Atlantic interdecadal climate variability is crucial for improving climatic prediction over the coming decades. Here the effect of thermal coupling on the leading energy sources of the interdecadal variability of the ocean-atmosphere system is examined by means of a stochastically-forced idealized coupled model. The effect of coupling is quantified from a comparison of the buoyancy variance budget of coupled and uncoupled model configurations. The simplicity of the model allows us to contrast the effect of coupling between a super-critical regime where the deterministic ocean dynamics drive the variability and a damped regime where noise forcing is central to its existence. The results show that changes in surface buoyancy fluxes act as a sink of temperature variance in the super-critical regime, and only become a source in the strongly damped regime. By contrast, internal ocean dynamics associated with the interaction of transient buoyancy fluxes with mean buoyancy gradients always act as a source of interdecadal variability. In addition to the reduced thermal damping effect in coupled integrations, thermal coupling with the atmosphere is shown to significantly increase the role of internal ocean dynamics in the variability, in particular in the regime where interdecadal modes are damped. Only for oceanic background states in the strongly damped regime do changes in surface buoyancy fluxes play a leading role in the upper ocean variability. A stochastically-forced coupled box model is proposed that captures the basic effect of thermal coupling on atmospheric and oceanic energy sources of variability.