In 36 climate change simulations associated with phases 3 and 5 of the Coupled Model Intercomparison Project (CMIP3 and CMIP5), changes in marine low cloud cover (LCC) exhibit a large spread, and may be either positive or negative. Here we develop a heuristic model to understand the source of the spread. The model’s premise is that simulated LCC changes can be interpreted as a linear combination of contributions from factors shaping the clouds’ large-scale environment. We focus primarily on two factors—the strength of the inversion capping the atmospheric boundary layer (measured by the estimated inversion strength, EIS) and sea surface temperature (SST). For a given global model, the respective contributions of EIS and SST are computed. This is done by multiplying (1) the current-climate’s sensitivity of LCC to EIS or SST variations, by (2) the climate-change signal in EIS or SST. The remaining LCC changes are then attributed to changes in greenhouse gas and aerosol concentrations, and other environmental factors. The heuristic model is remarkably skillful. Its SST term dominates, accounting for nearly two-thirds of the intermodel variance of LCC changes in CMIP3 models, and about half in CMIP5 models. Of the two factors governing the SST term (the SST increase and the sensitivity of LCC to SST perturbations), the SST sensitivity drives the spread in the SST term and hence the spread in the overall LCC changes. This sensitivity varies a great deal from model to model and is strongly linked to the types of cloud and boundary layer parameterizations used in the models. EIS and SST sensitivities are also estimated using observational cloud and meteorological data. The observed sensitivities are generally consistent with the majority of models as well as expectations from prior research. Based on the observed sensitivities and the relative magnitudes of simulated EIS and SST changes (which we argue are also physically reasonable), the heuristic model predicts LCC will decrease over the 21st-century. However, to place a strong constraint, for example on the magnitude of the LCC decrease, will require longer observational records and a careful assessment of other environmental factors producing LCC changes. Meanwhile, addressing biases in simulated EIS and SST sensitivities will clearly be an important step towards reducing intermodel spread in simulated LCC changes.