Shallow clouds are a major source of uncertainty in climate predictions. Several different sources of the uncertainty are possible—e.g., from different models of shallow cloud behavior, which could produce differing predictions and ensemble spread within an ensemble of models, or from inherent, natural variability of shallow clouds. Here, the latter (inherent variability) is investigated, using a simple model of radiative statistical equilibrium, with oceanic and atmospheric boundary layer temperatures, To and Ta, and with moisture q and basic cloud processes. Stochastic variability is used to generate a statistical equilibrium with climate variability. The results show that the intrinsic variability of the climate is enhanced due to the presence of shallow clouds. In particular, the on-and-off switching of cloud formation and decay is a source of additional climate variability and uncertainty, beyond the variability of a cloud-free climate. Furthermore, a sharp transition in the mean climate occurs as environmental parameters are changed, and the sharp transition in the mean is also accompanied by a substantial enhancement of climate sensitivity and uncertainty. Two viewpoints of this behavior are described, based on bifurcations and phase transitions/statistical physics. The sharp regime transitions are associated with changes in several parameters, including cloud albedo and longwave absorptivity/carbon dioxide concentration, and the climate state transitions between a partially cloudy state and a state of full cloud cover like closed-cell stratocumulus clouds. Ideas of statistical physics can provide a conceptual perspective to link the climate state transitions, increased climate uncertainty, and other related behavior.