An analysis of diabatic heating and moistening processes from 12 to 36 h lead time forecasts from 12 Global Circulation Models are presented as part of the “Vertical structure and physical processes of the Madden-Julian Oscillation (MJO)” project. A lead time of 12–36 h is chosen to constrain the large-scale dynamics and thermodynamics to be close to observations while avoiding being too close to the initial spin-up of the models as they adjust to being driven from the Years of Tropical Convection (YOTC) analysis. A comparison of the vertical velocity and rainfall with the observations and YOTC analysis suggests that the phases of convection associated with the MJO are constrained in most models at this lead time although the rainfall in the suppressed phase is typically overestimated. Although the large-scale dynamics is reasonably constrained, moistening and heating profiles have large intermodel spread. In particular, there are large spreads in convective heating and moistening at midlevels during the transition to active convection. Radiative heating and cloud parameters have the largest relative spread across models at upper levels during the active phase. A detailed analysis of time step behavior shows that some models show strong intermittency in rainfall and differences in the precipitation and dynamics relationship between models. The wealth of model outputs archived during this project is a very valuable resource for model developers beyond the study of the MJO. In addition, the findings of this study can inform the design of process model experiments, and inform the priorities for field experiments and future observing systems.