Nonlinear dynamics of a simple bead-spring glass-forming polymer were studied with molecular dynamics simulations. The energy response to sinusoidal variations in the temperature was tracked in order to evaluate the dynamic heat capacity. The amplitude dependence of the response is the focus of the current paper where pronounced nonlinear behavior is observed for large amplitudes in the temperature "driving force." We generalize the usual linear response analysis to the nonlinear regime so that higher order terms in the Fourier series of the energy response can be compactly analyzed. This is done by grouping all Fourier terms contributing to entropy generation into a "loss" contribution and the remainder yields the "storage" term. Finally, the bead-spring system is mapped onto three simpler models. First is a potential energy inspired "trap" model consisting of interconnected potential energy meta-basins and barriers. Second is the Tool-Narayanaswamy-Moynihan (TNM) model. Third is a version of the TNM model with a temperature dependent heat capacity. Qualitatively similar nonlinear behaviors are observed in all cases.