The school adjustment of children is the cornerstone of their development, and has been known to be influenced by a variety of factors. This study investigated the effects of peer relationships, theory of mind (ToM), hot executive function (hot EF), and cognitive ability on young children's school adjustment. Participants were 183 children with a mean age of 62.6 months attending ten kindergartens in Korea. Data was collected using the Preschool Adjustment Questionnaire, the Penn Interactive Peer Play Scale, three theory of mind tasks, two hot executive function tasks, and the Korean version of the Kaufman Assessment Battery for Children. School adjustment was found to correlate with peer relationships, cognitive ability, hot EF, and ToM. Using Hierarchical Regression analyses, hot EF was found to contribute unique variance in predicting school adjustment, even when variance due to peer relationships and cognitive abilities was excluded. This study has implications for identifying relevant variables that affect the school adjustment of young children, which can have a significant impact on future research on school adaptation.