The glass transition temperature ($T_g$) and conversion (${alpha}$) were measured for a diglycidyl ether of bisphenol A (DGEBA) epoxy/aromatic amine system incorporated with an organic-inorganic hybrid molecule, polyhedral oligomeric silsesquioxane (POSS). Samples isothermally cured at varying cure temperatures and times were analyzed by differential scanning calorimetry (DSC). $T_g$ vs. ln (time) data at an arbitrary reference were superposed by time-temperature shifts for the kinetically controlled reaction, and the shift factors were used to calculate an Arrhenius activation energy. Influence of POSS was investigated from $T_g$ vs. ${alpha}$ data, which in turn were fitted with DiBenedetto equation.