We discuss inherent thermometry in a Superconductor-Normal metal-Superconductor tunnel junction. In this configuration, the energy selectivity of single-particle tunneling can provide a significant electron cooling, depending on the bias voltage. The usual approach for measuring the electron temperature consists in using an additional pair of superconducting tunnel junctions as probes. In this paper, we discuss our experiment performed on a different design with no such thermometer. The quasi-equilibrium in the central metallic island is discussed in terms of a kinetic equation including injection and relaxation terms. We determine the electron temperature by comparing the micro-cooler experimental current-voltage characteristic with isothermal theoretical predictions. The limits of validity of this approach, due to the junctions asymmetry, the Andreev reflection or the presence of sub-gap states are discussed.