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Two-dimensional hybrid metal-halide perovskites (2D-MHPs) have emerged as important solution-processed semiconductors with favorable optical and electronic properties for diverse applications in photovoltaics, optoelectronics, and spintronics. The quasi-2D layered structures, featuring large acoustic impedance mismatches between the organic and inorganic sublattices, are expected to result in distinct and anisotropic thermal transport properties along the cross-plane and in-plane directions. Here, we introduce transducer-free vibrational-pump-visible-probe (VPVP) approaches that enable accurate quantification of anisotropic thermal transport properties in various archetypical single-crystalline 2D-MHPs. Specifically, using VPVP spectroscopy and VPVP microscopy, we measure the anisotropic thermal diffusivities of 2D-MHPs with systematically varied Pb-I octahedral layer thicknesses, as well as organic spacer types and lengths, revealing how these structural parameters alter the cross-plane and in-plane thermal transport properties in distinct ways. While diffuse interface scattering plays an important role in dictating cross-plane thermal transport, in-plane thermal transport is primarily determined by phonon transport within interconnected inorganic layers. Density functional theory incorporating four-phonon scatterings provides further insight into the low thermal conductivity and modest thermal conduction anisotropy in 2D-MHPs. Our work demonstrates a new all-optical and noncontact method, which requires minimal sample preparation and allows direct visualization of cross-plane and in-plane thermal transport, potentially compatible with sample environments. The demonstrated VPVP approaches can advance understanding of thermal transport in 2D-MHPs as well as wide-ranging hybrid and polymeric semiconductors beyond 2D-MHPs.