In thermal engineering, maintaining the temperature precisely at a desired setpoint is an essential objective for many processes. When heating actuators act locally and a few point sensors provide observations at different locations, the problem is complex. This communication deals with the control of a thermal system whose evolution is described by a parabolic partial differential equation (the domain is a thin steel plate subjected to heat sources on its upper surface, and to natural convection on its boundaries). The mathematical model remains valid in a 2D domain under the condition of negligible plate thickness. Equilibrium is reached when the combined effects of heat supplied by the sources and cooling induced by the surrounding environment balance out. The aim of this study is to achieve this state of equilibrium in a finite time by appropriately controlling the heat sources. The challenge of identifying these flows is addressed in the form of an inverse heat conduction problem (known to be ill-posed), and the implementation of the conjugate gradient regularization method is discussed.