  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, $T \lesssim 5~$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.
