Efficient heat dissipation in micro/nano electronics requires long-distance propagation of heat carriers operated above room temperature. However, thermal phonons - the primary heat carriers in dielectric nanomaterials - dissipate the thermal energy after just a few hundred nanometers. Theory predicts that the mean free path of surface phonon-polaritons (SPhPs) can be hundreds of micrometers, which may improve the overall dissipation of heat in nanomaterials. In this work, we experimentally demonstrate such long-distance heat transport by SPhPs. Using the 3 ω technique, we measure the in-plane thermal conductivity of SiN nanomembranes for different heater-sensor distances, membrane thicknesses, and temperatures. We find that thin nanomembranes support heat transport by SPhPs, as evidenced by an increase in the thermal conductivity with temperature. Remarkably, the thermal conductivity measured 200 μm away from the heater is consistently higher than that measured 100 μm closer. This result suggests that heat conduction by SPhPs is quasi-ballistically over at least hundreds of micrometers. Our findings pave the way for coherent heat manipulations above room temperature over macroscopic distances, which impacts the applications in thermal management and polaritonics.