Glass transition temperature (T-g) is a fundamental property of a polymer that defines its upper service temperature for structural applications and is often indicative of its other thermophysical features. This paper investigates how vapor-phase infiltration (VPI), which infuses polymers with inorganic species to create organic-inorganic hybrid materials, affects the material's glass transition temperature. We examine VPI of aluminum oxide (Al2O3 or AlOx) into poly(styrene-r-2-hydroxyethyl methacrylate) (PS-r-PHEMA) random copolymer thin films using trimethylaluminum (TMA) and water (H2O) precursors. These VPI precursors are intended to be unreactive toward the styrene monomer units and highly reactive toward the HEMA monomer units. Experiments were conducted on PS-r-PHEMA thin films (200 nm) spun-cast onto silicon wafers and infiltrated at 100 degrees C with 4 h exposure times. Copolymers with varying fractions of HEMA units were investigated, from 0 to 20.2 mol % HEMA. Volumetric swelling of the films after VPI and aluminum oxide film thicknesses after pyrolysis both confirm higher metal oxide loading in polymers with higher HEMA fractions. Tg was measured by tracking film thickness as a function of temperature using spectroscopic ellipsometry. The glass transition temperature is found to increase significantly with metal oxide loading. Copolymers with 0.0, 3.0, 7.7, 11.5, and 20.2% HEMA units experienced 6, 8, 22, 37, and 46 degrees C increases in Tg, respectively. Changes in T-g at low HEMA compositions fit the Fox-Loshaek model for cross-linking phenomena, which, along with a dissolution study on these materials, suggests that VPI is cross-linking the PS-r-PHEMA polymer. This study demonstrates that VPI is useful for altering the thermophysical and thermochemical properties of polymer materials, with applicability to many form factors including thin films, coatings, membranes, foams, fibers, and fabrics.