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 the scientific literature based on various approaches, tools, and techniques. The present study proposes a new approach to numerical modeling and simulation based on the Holm contact theory, aiming to study the dependence between the electric potential and the temperature within an electrical contact. Structured in five 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, electric field amplitude, variation of the electrical potential along the current path, temperature gradient, and dependence of temperature along the contact elements edges were obtained by simulation, and are graphically represented. The results show that the temperature increase follows a parabolic curve, and that for values higher than 4 mV of voltage drop, the temperature of the contact increases to 79.25 degrees (and up to 123.81 degrees for 5 mV) over the ambient temperature, thus the integrity of insulation can be compromised. These values are close (10–12%) to the analytically calculated ones, and also in line with research assessed in the literature review.