The hot wire technique is widely used to determine the thermal properties of materials. Commonly, this technique is developed for considered infinite radius of cylindrical mediums. Here, we propose an analytical solution of the heat conduction problem in an insulated finite sample. The derived temperature solution is found mathematically to be non-regular convergent series, and lead to avoid the assumption of infinite geometries, difficult to realize in practice. The first part of this paper concerns the study of the calculability of this series. The second one deals with the thermal properties estimation. The sensitivity study shows that the estimation procedure is feasible either using the concept of the time of the maximum rising temperature or, when exploring large time measurements, using the least squares minimisation that has an equivalent pure graphical procedure.