We
studied the physical aging of glycerol in response to upward
temperature steps of amplitude ranging from 0.3 to 18 K. This was
done using a specially designed experimental setup allowing quick
heating of a liquid film while measuring the evolution of its dielectric
properties. Despite the nonlinear evolution of these observables for
large steps, a fictive temperature could be obtained. In the case
of moderate step amplitudes, we checked that the material time approach
in its simplest form, the single parameter aging (SPA), applies well.
The memory kernel extracted from the quasi-linear regime was used
to test its frontiers of validity for significant step amplitudes.
We showed that the observations deviate from the prediction of the
material time framework and of SPA simultaneously. As these approaches
link aging to equilibrium dynamics, our results help set the bounds
beyond which new theoretical arguments are needed.