The nosie voltage found at the terminals of an electric dipole antenna immersed in a hot plasma is calculated. The plasma is assumed stable and at rest. It is described as made of two maxwellian electron populations. A grid of calculated nose spectra is presented in normalized coordinates, and we give analytical expression valid for frequencies much lower than the plasma frequency fp or close to the noise peak. The antenna impedance is also calculated; in contrast to the noise spectrum, it is found to be very weakly dependent upon the hot population parameters. From these results one can calculate the response of a receiving system, thus enabling the actual measurment of the plasma parameters from the noise spectrum. Using ISEE 3 SBH experimental data, it is shown that the observations do fit the theoretical predictions over most of the frequency range. Plasma parameters are obtained and found in good agreement with results from the Los Alamos plasma analyzer on the same spacecraft. It appears that the high energy tail of the paritcle distribution function accounts for the peak noise voltages of several times 10-12V2Hz-1 found at the terminals of a 45-m half-length dipole. The interpretation of these observations does not therefore require an unstable plasma. We discuss these results and show that more work should be done to explain an unpredicted increase of the spectrum below fp and to explain the weak spin modulation. Solving these remaining problems requires the introduction of ions and of the bulk and/or drift velocity into the calculations. Appendix A contains a partial justification of the assumption of a triangular current distribution on the antenna. The calculations are presented in appendix B.