We propose a mesoscopic thermometer for ultrasensitive detection based on the proximity effect in superconductor-normal metal (SN) heterostructures. The device is based on the zero-bias anomaly due to the inelastic Cooper-pair tunneling in an SNIS junction (I stands for an insulator) coupled to an ohmic electromagnetic (EM) environment. The theoretical model is done in the framework of the quasiclassical Usadel Green's formalism and the dynamical Coulomb blockade. The usage of an ohmic EM environment makes the thermometer highly sensitive down to very low temperatures, T 5 mK. Moreover, defined in this way, the thermometer is stable against small but nonvanishing voltage amplitudes typically used for measuring the zero-bias differential conductance in experiments. Finally, we propose a simplified view, based on an analytic treatment, which is in very good agreement with numerical results and can serve as a tool for the development, calibration, and optimization of such devices in future experiments in quantum calorimetry.