The paper considers the method of correction of thermographic images (thermograms) obtained by recording in the infrared range of radiation from the surface of the object under study using a thermal imager. A thermogram with a certain degree of reliability transmits an image of the heat-generating structure inside the body.We performed the mathematical correction of images on a thermogram, based on an analytical continuation of the stationary temperature distribution as a harmonic function from the surface of the object under study towards the heat sources. The continuation is carried out by solving an ill-posed mixed problem for the Laplace equation in a cylindrical region of rectangular cross-section. To construct a stable solution to the problem, the principle of the minimum of the Tikhonov smoothing functional is used.