We show theoretically that the electron density and temperature of a plasma could be deduced from the measurements of the transfer impedance between two small dipole antennae, each much shorter than a Debye length, separated by a distance of ten or more Debye lengths. In contrast to the quadripole probe, this ‘double-dipole probe’ relies on not producing perturbations in the plasma, rather than on minimizing their effects. The plasma is assumed to be warm and isotropic, and the motion of the ions is neglected. First, it is shown that, in a Maxwellian plasma, the frequency response of a double-dipole probe is easier to interpret than that of a quadripole probe with the customary square layout. Then, in a second step, the transfer impedance of the former probe is calculated in a Cauchy plasma, and the results are compared with those previously obtained in a Maxwellian plasma. By so doing, we show that, for large distances between the dipoles, the real part of the transfer impedance is sensitive to the form of the tail of the distribution function.