In the paper the parametric inverse problem is considered. On the basis of knowledge of time-dependent course of temperature at the selected points from the interior of domain the volumetric specific heat is identified. In order to solve the inverse problem formulated the least squares criterion in which the sensitivity coefficients appear has been applied. The basic problem and additional ones (determining the sensitivity coefficients) are solved using the 1st scheme of the BEM. In the final part of the paper the results of computations are shown.