Ocean conditions are known to play a critical role in the intensification of tropical cyclones (TCs). However, the relative roles of ocean temperature and salinity stratification for ocean mixing and TC-induced sea surface temperature (SST) cooling have remained unclear. Furthermore, there has been limited quantification of which factors, in terms of TC characteristics and pre-storm ocean state, are the most important in controlling the amount of cooling. To investigate the mechanisms that control the amount of ocean cooling under a TC, we use a one-dimensional mixed layer model initialized with a variety of realistic oceanic profiles and forced with different simulated tropical cyclones. We then compare our findings to observations and reanalyses. Results consistently show that the thermodynamic effect (changes in vertical temperature gradient with density gradient held constant) is 2-3 times that of the mixing effect (changes in density stratification with temperature stratification held constant) and that translation speed and storm size are the two most important factors for SST cooling, followed by temperature stratification. These results emphasize the often overlooked role of storm size. We also investigate the potential predictability of TC-induced SST cooling using TC and ocean predictors in a linear regression model. It is found that this simple method, trained on observations, performs as well as more complex methods.