Random copolymers usually considered as dynamically homogeneous with a single glass temperature can show dynamic heterogeneity by appropriate choice of their repeat units. Random copolymers based on polymethacrylates with polyhedral oligomeric silsesquioxane (POSS) moieties as side groups substituted with seven isobutyl ((i-Bu)(7)POSS-OSiMe2(CH2)(3)-MA) and 2,4,4-trimethylpentyl ((i-C8H17)(7)POSS-OSiMe2(CH2)(3)-MA) groups were synthesized and studied by dielectric spectroscopy, density functional theory, differential scanning calorimetry, and rheology. Two distinct relaxation processes were found by dielectric spectroscopy giving rise to two glass temperatures. In addition, rheology revealed significant broadening of the viscoelastic functions leading eventually to the failure of time-temperature superposition for all copolymer compositions. These results provide signatures of dynamic heterogeneity in a random copolymer.