Electrical contacts are important circuit components with diverse industrial applications, and their failure can lead to multiple unwanted effects. Hence, the behavior of electrical contacts is a widely studied topic in scientific literature based on various approaches, tools, and techniques. The present study proposes a numerical modeling and simulation approach based on the Holm contact theory to study the dependence between the electric potential and the temperature within an electrical contact. Structured in 5 sections, the research was conducted using COMSOL Multiphysics software and its solid-state mechanics, electric current, and heat transfer modules in order to highlight contact behavior from mechanical, electrical and thermal points of view: the von Mises stress, contact force, the electric field amplitude, the variation of the electrical potential along the current path, the temperature gradient, and dependence of temperature along the contact elements edges were obtained by simulation and graphically represented. The results are in line with the expectations and with past research that was studied in the literature review.