Thermal conductance measurements are sensitive to both charge and chargeless energy flow and are an essential measurement technique in condensed-matter physics. For two-dimensional topological insulators, the determination of thermal Hall (transverse) conductance and thermal longitudinal conductance is crucial for the understanding of topological order in the underlying state. Such measurements have not been accomplished, even in the extensively studied quantum Hall effect regime. Here we report a local power measurement technique that we use to reveal the topological thermal Hall conductance, going beyond the ubiquitous two-terminal conductance. For example, we show that the thermal Hall conductance is approximately zero in the v = 2/3 particle-hole conjugated state. This is in contrast to the two-terminal thermal conductance that gives a non-universal value that depends on the extent of thermal equilibration between the counter-propagating edge modes. Moreover, we demonstrate the utility of this technique in studying the power carried by the current fluctuations of a partitioned edge mode with an out-of-equilibrium distribution.