ABSTRACTMany climate models have problems in simulating the sea surface temperature (SST) in the tropical Indian Ocean (TIO). The Coupled Model Inter‐comparison Project Phase 5 (CMIP5) models, in general, underestimate SST over the entire TIO region. This study examines the SST evolution during spring to summer transition months (May and June) over the Arabian Sea (AS) region in the historical simulations of 13 CMIP5 models and the Climate Forecasting System coupled models CFSv1 and CFSv2. The annual cycle of SST shows that the summer monsoon cooling is not adequately captured by many models. Based on the state of June SST tendency, models have been divided in to three groups, the first group (G1) consists of models having stronger than observed cooling, second group (G2) considers models having closer to observed cooling and the third group (G3) includes models having lesser than observed cooling. Mixed layer heat budget analysis revealed that atmospheric flux is mainly responsible for unrealistic SST warming in most of the G3 models during June. The vertical mixing and horizontal advection contribute considerably to the SST cooling in summer (June) especially for G1 and G2 models. On the other hand, spring warming in all the models is consistently forced by the surface heat flux. It is also found that the monsoon low‐level jet (LLJ) is not accurately represented in most of the models. The misrepresentation of LLJ causes bias in the oceanic processes leading to unrealistic SST evolution in many models. One way of LLJ affecting the oceanic processes is by modulating mixed layer depth (MLD). It is observed in general that the models with deeper MLD display strong SST cooling. The model deficiency in representing AS SST is speculated to be a major limiting factor in capturing the monsoon rainfall in the current coupled models. The proper simulation of AS SST is therefore very crucial for the accurate representation of Indian summer monsoon precipitation.