High heat fluxes generated in electronics and semiconductor packages require materials with high thermal conductivity to effectively diffuse the heat and avoid local hotspots. Engineered heat spreading materials typically exhibit anisotropic conduction behavior due to their composite construction. The design of thermal management solutions is often limited by the lack of fast and accurate characterization techniques for such anisotropic materials. A popular technique for measuring the thermal diffusivity of bulk materials is the Ångstrom method, where a thin strip or rod of material is heated periodically at one end, and the corresponding transient temperature profile is used to infer the thermal diffusivity. However, this method is generally limited to the characterization of one-dimensional samples and requires multiple measurements with multiple samples to characterize anisotropic materials. Here, we present a new measurement technique for characterizing the isotropic and anisotropic in-plane thermal properties of thin films and sheets as an extension of the one-dimensional Ångstrom method and other lock-in thermography techniques. The measurement leverages non-contact infrared temperature mapping to measure the thermal response from laser-based periodic heating at the center of a suspended thin film sample. Uniquely, our novel data extraction method does not require precise knowledge of the boundary conditions. To validate the accuracy of this technique, numerical models are developed to generate transient temperature profiles for hypothetical anisotropic materials with known properties. The resultant temperature profiles are processed through our fitting algorithm to extract the in-plane thermal conductivities without knowledge of the input properties of the model. Across a wide range of in-plane thermal conductivities, these results agree well with the input values. Experiments demonstrate the approach for a known isotropic reference material and an anisotropic heat spreading material. The limits of accuracy of this technique are identified based on the experimental and sample parameters. Further standardization of this measurement technique will enable the development and characterization of engineered heat spreading materials with desired anisotropic properties for various applications.