The development of a novel approach to the well-known Angstrom´s method for the measurement of the thermal diffusivity is reported. In this method, the diffusivity is determined from the damping and the phase shift of a periodic thermal signal during its propagation along the specimen. The propagation can be easily monitored by infrared thermography. In general, a non-contact source is used to apply the signal. In the present work, however, a direct-contact source is employed, with a temperature-oscillation signal supplied on a portion of one of the two main surfaces of the specimen, where a homogeneous contact can be yielded by using a proper contact pressure. Such practice implies that the measures of surface temperature can be used to estimate the diffusivity only beyond a certain distance from the source, where the wave-front of the temperature oscillation within the specimen becomes plane and perpendicular to the main surfaces. This distance is investigated here, to establish a general rule for the performance of the experiments. A thermoelectric device based on the Peltier effect is employed as the thermal source. The main difficulty about its use is to obtain a perfectly harmonic and well-balanced thermal signal. This is necessary to avoid a complex processing of the experimental data, and it can be achieved by supplying a current with a properly-chosen time-evolution pattern. Such an approach, which is built upon previous work, is here enhanced by improving the underlying analytical model.