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This communication focuses on an inverse problem of the physical phenomena which can be described by the partial differential equation. Especially, an unknown parameter identification process of the heat conduction problem in the thermal domain related to mobile heating source tracking is investigated. To do this, an iterative minimization of a quadratic cost-function based on the conjugate gradient method is widespread since this algorithm provides regularization properties for an estimation of the trajectory of a mobile heating source. Furthermore, another identification method is proposed by using the conjugate gradient method combined with the sensitivity problem of the sensor network. A quasi-online adaptation of this numerical method aims to identify the unknown characteristics with a small delay after the required temperature measurements by selecting the better sensors locations, this could also reduce the computational time. This approach offers the opportunity to move mobile sensors in order to increase the overall sensitivity and thus to improve the quality of the identification which is a shorter delay and better accuracy.