Based on fluctuational electrodynamics, we reveal a dimensional crossover in far-field thermal radiation between subwavelength gold membranes. As the membrane thickness decreases from the bulk to the nanoscale, we observe a transition from three-dimensional to two-dimensional heat transfer, which is characterized by a distinct minimum plateau in thermal conductance for intermediate subwavelength thicknesses. This behavior, absent in polar dielectrics, stems from the coupling and decoupling of long-range surface plasmon-polariton modes. The thermal conductance exhibits a $T^3$ dependence for thick membranes at high temperature and transitions to a $T^2$ dependence for ultrathin films at low temperature, reflecting the dimensional shift in the photon density of states. Notably, the minimum plateau falls below the black-body limit, demonstrating the potential for tailoring far-field thermal radiation in metallic nanostructures through dimensional confinement and plasmonic effects.

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• Heat radiation
• Heat transfer
• Phonon polariton
• Thermal conductivity
• Energy applications
• Metals
• Multilayer thin films
• Nanotechnology