A novel model of the dense z-pinch of a plasma focus (PF) discharge is presented, assuming Gaussian radial distributions of density and temperature inside the pinch. The model is used to assess the temperature, size and lifetime of the focus conflating with available experimental data gathered from discharges in Deuterium performed in the PF PACO with three cathode configurations. The resulting estimations were mean pinch temperatures between 1 and 12 keV, and pinch durations between 10 and 120 ns, each magnitude decreasing and increasing with the filling pressure, respectively. Moreover, the relation found between the mean pinch radius and temperature, and , is consistent with an adiabatic compression given by mm keV3/4. The estimated width of the Gaussian profile is in agreement with spectroscopic images obtained in another small device.