For large linear heat conduction systems, it is proposed here to solve an inverse heat conduction problem (IHCP) that consists in the identification of several time-varying thermal solicitations from simulations of measured temperatures. For this inversion, instead of using a detailed model of large size, this one is first transformed into a reduced model. The: latter is built with identified dominant eigenmodes of the system leading to a reduced state representation that links the inputs (unknown solicitations) to the outputs (simulated temperatures). The procedure is sequential and uses future time steps. At first, a numerical 2D IHCP is provided: two time-varying heat flux densities are estimated from various positions of two sensors. A specific study on static and dynamic sensitivities is made. All example of a 3D IHCP is also given. The method is particularly interesting in this last case where, at each time step, the resolution ufa system of order 9 (the reduced model) takes the place of a system of order 1331 (the detailed model).