An analytical solution has been developed for the curing of thick polymer composite laminates that shows how the temperature profile responds to arbitrary changes to the material properties and process parameters and that curing with slow reactions and a low exotherm temperature is impossible if the Damköhler number is above a well-defined limit. The thermal runaway criterion can be recast as a criterion for the maximum allowable thickness of the laminate. The thermal runaway criterion was found to agree well with some results for thick laminates from the literature, but the peak temperature in the laminate was underpredicted for stable conditions. The model has a constant that can be adjusted to improve the peak temperature prediction, but more validation data is needed before the model can be optimized to simultaneously predict the peak temperature and thermal runaway with high accuracy.