Intermolecular noncovalent forces between polymer chains influence the mobility and glass-transition temperature (T-g), where weaker interchain interactions, all else being the same, typically results in lower bulk polymer T-g. Using molecular dynamics simulations, here we show that this relation can become invalid for supported ultrathin films when the substrate polymer interaction is extremely strong and the polymer polymer interactions are much weaker. This contrasting trend is found to be due to a more pronounced substrate-induced appreciation of the film T-g for polymers with weaker intermolecular interactions and low bulk T-g. We show that optimizing this coupling between substrate adhesion and bulk T-g maximizes thin film T-g, paving the way for tuning film properties through interface nanoengineering.