Heat transport by acoustic phonons in two-dimensional (2D) materials is fundamentally different from that in 3D crystals because the out-of-plane phonons propagate in a unique way that strongly depends on tension and bending rigidity. Here, using optomechanical techniques, we experimentally demonstrate that the heat transport time in freestanding graphene membranes is significantly higher than the theoretical prediction, and decreases by as much as $33\%$ due to an electrostatically induced tension of 0.07 $\mathrm{N}/m$. Using phonon scattering and Debye models, we explain these observations by the tension-enhanced acoustic impedance match of flexural phonons at the boundary of the graphene membrane. Thus, we experimentally elucidate the tunability of phononic heat transport in 2D materials by tension, and open a route towards electronic devices and circuits for high-speed control of temperature at the nanoscale.

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• Heat transfer
• Mechanical & acoustical properties
• Thermal expansion
• Thermal properties
• Thermomechanical effects
• Graphene
• Interfaces
• Nanomechanical devices