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We present a method to measure the critical temperature of the island of asuperconducting single electron transistor. The method is based on a sharpchange in the slope of the zero-bias conductance as a function of temperature.We have used this method to determine the superconducting phase transitiontemperature of the Nb island of an superconducting single electron transistorwith Al leads. We obtain $T_\mathrm{c}^\mathrm{Nb}$ as high as 8.5 K and gapenergies up to $\Delta_\mathrm{Nb}\simeq 1.45$ meV. By looking at the zero biasconductance as a function of magnetic field instead of temperature, also thecritical field of the island can be determined. Using the orthodox theory, wehave performed extensive numerical simulations of charge transport propertiesin the SET at temperatures comparable to the gap, which match very well thedata, therefore providing a solid theoretical basis for our method.

Method for finding the critical temperature of the island in a SET structure