We introduce a simple model for the time-dependent evolution of tropical "hot spots", or localized regions where the sea surface temperature (SST) becomes unusually high for some period of time. The model consists of a single-column atmospheric model under convective adjustment with a simple parameterization of cloud-radiative feedbacks, coupled to an ocean mixed layer. For plausible parameter values, the steady model solutions can become unstable to time-dependent oscillations, which are studied both using linear stability analysis and explicit time-dependent nonlinear simulation. The oscillations typically have periods ranging from intraseasonal to subannual. For parameter values only slightly beyond the threshold for instability, the oscillations become strongly nonlinear, and have a pulse-like, recharge-discharge character. The basic instability comes from the longwave radiative feedback of high clouds, which tends to enhance preexisting deep convection. This is counteracted by the shortwave radiative feedback of the same clouds, which eventually reduces the SST enough to render the model stable to deep convection, shutting it off. At that point the SST begins warming again under the resulting clear skies, starting the cycle over.

We also examine the forced response of the model, in a stable regime, to an imposed atmospheric oscillation. This is meant to crudely represent forcing by an atmospheric intraseasonal oscillation which would exist even in the uncoupled system, but is modified by coupling, as has been simulated in general circulation models. In this context, the model's response as a function of mixed layer depth maximizes around 20 meters, close to the observed value in the western Pacific warm pool, suggesting that the mixed layer depth there is optimal for this sort of coupled interaction.