We report that the fractions of "bonded" or "unbonded" monomers at a filler interface dictate the composition dependence of the glass transition temperatures (Tg) of polyhedral oligomeric silsesquioxane (POSS)-containing nanocomposites. Tg is arguably the single most important material property; however, predicting Tg in nanocomposites is often challenging because of confounding interfacial effects. To this end, we design a model nanocomposite to systematically study Tg of nanocomposites by leveraging the "all-interfacial" nature of ultrasmall POSS fillers loaded into random copolymers of styrene and 2-vinylpyridine (2VP). The amine-functionalized POSS forms hydrogen bonds only with 2VP, which behaves as a "bonded" monomer. The influence of copolymer composition and POSS loading on the Tg of this model composite is successfully explained by a Fox equation framework. This model also captures the Tg increase of other POSS-based polymer composites and potentially directs the future design of nanocomposite materials with tailored Tg.