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A key component for optical on-chip communication is an efficient light source. However, to enable low energy per bit communication and local integration with Si CMOS, devices need to be further scaled down. In this work, we fabricate micro- and nanolasers of different shapes in InP by direct wafer bonding on Si. Metal-clad cavities have been proposed as means to scale dimensions beyond the diffraction limit of light by exploiting hybrid photonic-plasmonic modes. Here, we explore the size scalability of whispering-gallery mode light sources by cladding the sidewalls of the device with Au. We demonstrate room temperature lasing upon optical excitation for Au-clad devices with InP diameters down to 300 nm, while the purely photonic counterparts show lasing only down to 500 nm. Numerical thermal simulations support the experimental findings and confirm an improved heat-sinking capability of the Au-clad devices, suggesting a reduction in device temperature of 450 - 500 K for the metal-clad InP nanodisk laser, compared to the one without Au. This would provide substantial performance benefits even in the absence of a plasmonic mode. These results give an insight into the benefits of metal-clad designs to downscale integrated lasers on Si.