A method of determining a thermal conductivity and a thermal diffusivity of a material comprises exposing a specimen comprising a substrate of a material and a metallic film over the substrate to an amplitude modulated pump laser beam comprising electromagnetic radiation having a first wavelength and a first modulation frequency to form a pump spot on the metallic film. The specimen is exposed to a probe laser beam comprising electromagnetic radiation having a second wavelength to form a probe spot on the metallic film. A phase shift between the pump laser beam and a reflected probe laser beam is measured while scanning the pump spot relative to the probe spot. A modulation frequency of the pump laser beam is changed to a second modulation frequency and the pump spot is scanned relative to the probe spot while detecting the phase shift. A phase profile of the material is measured and a continuum-based model is fit to the phase profile. Related microscopes and related methods are also disclosed.