This paper has the purpose of exposing the physical theoretical foundations and experimental results that have been obtained after 4 years of research and experimentation with fires in electrical conductors. It is based on the concept of transformation of electric power in thermal, in the moment of the electrical conduction, which commonly is known as "Joule Effect". A review of the state of the art is presented, concerning the models research of heating of conductors and applications of modeling that might be used in fire protection engineering and electricity, to create advances in the comprehension of facts. It is proposed the hypothesis that fires that take place with an electric element as a primary source of energy, not necessarily initiate when an electric arc or short circuit exists, but they can initiate long before, when this element is heated according to the Joule Effect and this is enough for ignite some material around or to affect some part of the conductor element itself. A scientific general analysis is given on the way fires are generated the by electrical causes, and a new mathematical model is proposed as a contribution to the scientific field of electricity and fire protection science.