Lattice vibrations govern the propagation of heat in materials, and investigating their dynamics through time-resolved phonon dispersion measurements would provide insight into these excitations and their interactions. However, time-resolved measurements that directly resolve the phonon dispersion at the nanoscale have not been previously demonstrated. Momentum-resolved vibrational electron energy loss spectroscopy (EELS) provides access to phonon energies and momenta with nanoscale spatial resolution. Here, we combine momentum-resolved vibrational EELS with pulsed laser heating and synchronised gated electron detection to observe the phonon dispersion of graphite during controlled heating and cooling on the microsecond timescale. Recording both the gain and loss spectra at defined times relative to laser excitation, we determine the temperature at each time delay and follow changes to the phonon branches as a function of temperature. The momentum-resolved spectra reveal a decrease in energy of the optical phonon branch with increasing temperature accompanied by an increase in peak width. These changes are consistent with temperature-dependent phonon renormalisation and scattering associated with anharmonic interactions. The approach is compatible with detector gating on timescales down to 50 ns, providing a route towards extending these measurements to faster dynamics. This work demonstrates time-resolved phonon dispersion spectroscopy using vibrational EELS and provides a route towards probing temperature-dependent phonon dynamics at the nanoscale with simultaneous energy and momentum resolution.