A 3-D mortar domain decomposition approach based on the cell method (CM) for analyzing electro-thermal contact problems is presented. The computational domain is subdivided into non-overlapping regions discretized according to the CM, where variables and field equations are expressed directly in integral form suitable for coupling the contact problem to the electro-thermal one in the bulk regions. Voltage and temperature discontinuities at contact interfaces are modeled by diagonal conductance matrices. The electrical and thermal continuity between contacting regions is enforced by means of dual Lagrange multipliers. Nonlinear equations are cast into a saddle-point form ensuring existence and uniqueness of the solution. Problem size is reduced by the Schur complement approach. A 3-D finite-element software for multiphysics problems is used to validate the mortar cell method.