This paper deals with an inverse problem, which consists of the experimental identification of line heat sources in a homogeneous solid in transient heat conduction. The location and strength of the line heat sources are both unknown. For a single source we examine the case of a source which moves in the system during the experiment. The identification procedure is based on a boundary integral formulation using transient fundamental solutions. The discretized problem is non-linear if the location of the line heat sources is unknown. In order to solve the problem we use an iterative procedure to minimize a cost function comparing the modelled heat source term and the measurements. The proposed numerical approach is applied to experimental 2D examples using measurements provided by an infrared scanner for surface temperatures and heat fluxes. In some particular examples, internal thermocouples can be used. A time regularization procedure associated to future time-steps is used to correctly solve the ill-posed problem.