  Nanomechanical resonators have emerged as sensors with exceptional
sensitivities. These sensing capabilities open new possibilities in the studies
of the thermodynamic properties in condensed matter. Here, we use mechanical
sensing as a novel approach to measure the thermal properties of
low-dimensional materials. We measure the temperature dependence of both the
thermal conductivity and the specific heat capacity of a transition metal
dichalcogenide (TMD) monolayer down to cryogenic temperature, something that
has not been achieved thus far with a single nanoscale object. These
measurements show how heat is transported by phonons in two-dimensional
systems. Both the thermal conductivity and the specific heat capacity
measurements are consistent with predictions based on first-principles.
