In the realm of thermal systems governed by parabolic partial differential equations, achieving precise control and trajectory of mobile heating sources creates a formidable challenge, particularly in the presence of moving disturbances. This study delves into the thermal dynamics of a 3D steel plate, typically analyzed in 2D due to its negligible thickness. Initially, the plate maintained equilibrium through natural convection and heat fluxes subjected to its surface. However, mobile disturbances existence has disrupted this balance, significantly across a fixed array of sensors. To track and reject these perturbations, the identification of control and trajectory of a mobile disk is studied. This process is treated as an inverse heat conduction problem, known as ill-posed. Consequently, the conjugate gradient regularization method is applied.