Introduction: Plasmonic photothermal therapy (PPTT) with noble metal nanoparticles (NPs) have gained great relevance as less invasive platforms in the treatment of adenocarcinoma-type cancer tumors. The PPTT uses laser radiation to generate plasmonic effects in NPs that are distributed in the cancerous tissue, producing hyperthermia and cell death by apoptosis. Objective: To obtain two-dimensional temperature distributions and the associated cell damage distributions in tumoral tissue subjected to PPTT. Method: A numerical methodology based on Radial Basis Functions (RBFs) is implemented for solving the Pennes or bioheat equation and the Arrhenius and Three-state models for cellular damage estimation. The developed, validated and applied numerical methodology is based on the method of approximate particular solutions in local formulation (LMAPS). Results: The capability to solve problems with variable sources, multiple regions and different types of boundary conditions is shown by the comparison with OpenFOAM computational tool based on finite volume method and numerical results reported in the literature. This is performed by solving hypothetical situations of heat transfer in tissues including 1D and 2D domains with metabolic sources, perfusion term and radiation thermal conversion. Conclusions: The developed methodology is applied to a situation of PPTT in superficial tissue, from laser energy distribution description to the local percentage of cellular damage. This numerical methodology is the basis of the analysis, optimization and design of PPTT application processes in clinical environments considering its potential to solve complex geometries, time-varying boundary conditions and parameters and domains with multiple regions.