In the last two decades, tremendous research has been conducted on the discovery, design and synthesis, characterization, and applications of two-dimensional (2D) materials. Thermal conductivity and interface thermal conductance/resistance of 2D materials are two critical properties in their applications. Raman spectroscopy, which measures the inelastic scattering of photons by optical phonons, can distinct a 2D material's temperature from its surrounding materials', featuring unprecedented spatial resolution (down to the atomic level). Raman-based thermometry has been used tremendously for characterizing the thermal conductivity of 2D materials (suspended or supported) and interface thermal conductance/resistance. Very large data deviations have been observed in literature, partly due to physical phenomena and factors not considered in measurements. Here, we provide a critical review, analysis, and perspectives about a broad spectrum of physical problems faced in Raman-based thermal characterization of 2D materials, namely interface separation, localized stress due to thermal expansion mismatch, optical interference, conjugated phonon, and hot carrier transport, optical-acoustic phonon thermal nonequilibrium, and radiative electron-hole recombination in monolayer 2D materials. Neglect of these problems will lead to a physically unreasonable understanding of phonon transport and interface energy coupling. In-depth discussions are also provided on the energy transport state-resolved Raman (ET-Raman) technique to overcome these problems and on future research challenges and needs.