Johnson Noise Thermometry (JNT) can be regarded as a quite well established technique for the evaluation of the temperature. It relays on the accurate estimation of the voltage noise across a resistor, that acts as a sensor, and on the knowledge of the resistance of the sensor itself. In order to perform a temperature measurement, therefore, the resistance of the sensor has to be measured with a high accuracy multimeter and afterwards, the voltage noise across its ends has to be estimated in the assumption that the resistance does not change with time and is independent of frequency. In this paper we present a new approach for JNT that is based on a four channel cross correlation technique that allows, at least in principle, to estimate the temperature of a passive bipole from noise measurements only, as the power spectra of the current noise of the bipole and the real and imaginary part of its admittance can all be obtained from a proper elaboration of the acquired noise spectra. In particular, as the real part of the bipole admittance can be estimated as a function of the frequency, the limitation of resorting to purely resistive bipoles is also removed. Preliminary results demonstrating the effectiveness of the approach we propose are reported in this paper. The most important technical limitations that, at present, prevent the new approach to compete with the most advanced technique developed for the case of the conventional JNT are also discussed.