Applicability and limits of time-resolved rheometry have been analyzed for polymers which undergo change during a theological measurement. Processes such as gelation, phase transition, polymerization or decomposition affect the molecular mobility in these polymers and therefore the rheological experiment. We propose to choose the well known effect of heating (or cooling) during the relaxation and analyze it as a paradigm for rheometry on samples with changing molecular mobility. The temperature change does not cause permanent changes in sample structure, but it affects the molecular mobility and it significantly interferes with the measurement if the temperature changes occur too fast. In this study, time-resolved mechanical spectroscopy (TRMS) was used to experimentally investigate the effect of heating on the relaxation behavior of a typical polycarbonate sample. Each data point in a cyclic frequency sweep (CFS) was taken at a different state of the material; the data were interpolated using an interactive computer program. In this fashion, a single TRMS experiment yielded a master curve over eight decades. A model for relaxation under non-isothermal conditions showed the limitations of TRMS. It could be demonstrated that TRMS worked well for sufficiently small mutation numbers, i.e., for sufficiently small changes during the measurement. A critical mutation number of 0.9 was determined for the non-isothermal case beyond which the material response became non-linear. This corresponds to a calculated relative change of the shear stress amplitude of about 90%.