  We establish heat kernel upper bounds for a continuous-time random walk under
unbounded conductances satisfying an integrability assumption, where we correct
and extend recent results by the authors to a general class of speed measures.
The resulting heat kernel estimates are governed by the intrinsic metric
induced by the speed measure. We also provide a comparison result of this
metric with the usual graph distance, which is optimal in the context of the
random conductance model with ergodic conductances.
