  Thermal properties of suspended single-layer graphene membranes are
investigated by characterization of their mechanical motion in response to a
high-frequency modulated laser. A characteristic delay time $\tau$ between the
optical intensity and mechanical motion is observed, which is attributed to the
time required to raise the temperature of the membrane. We find, however, that
the measured time constants are significantly larger than the predicted ones
based on values of the specific heat and thermal conductivity. In order to
explain the discrepancy between measured and modeled tau, a model is proposed
that takes a thermal boundary resistance at the edge of the graphene drum into
account. The measurements provide a noninvasive way to characterize thermal
properties of suspended atomically thin membranes, providing information that
can be hard to obtain by other means.
