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The Rosenthal steady-state analytical solution for the temperature distribution caused by a moving point heat source on a semi-infinite, homogeneous, isotropic solid has been extensively used in modeling metallurgical processes, e.g., arc welding. This study develops a three-dimensional analytical closed-form solution for the temperature field induced by a point heat source moving across a semi-infinite orthotropic solid. The formulation accommodates arbitrary orientations of the heat source's motion relative to the material's in-plane principal axes and is extended to solids with finite thickness. Subsequently, using the superposition of the linear solutions, a general methodology is proposed to predict the temperature distribution resulting from an arbitrarily distributed heat source. Verification of the closed-form solution and validation of the distributed heating condition against finite element simulations demonstrate excellent agreement. The analytical framework offers potential for thermal modeling of processing methods used for polymeric composites, e.g., additive manufacturing and continuous welding of thermoplastic composites.