Inverse methods can be used in solidification and related processes for the estimation of boundary conditions or physical properties of materials. For heat flow problems, these methods are based upon a minimisation of the errors between calculated and measured temperatures at given locations and times of the space-time domain, the calculated values being obtained from a numerical solution of the heat flow equation. In the present case, a maximum a posteriori technique has been implemented into a finite element code. This method is then applied to several situations for the determination of : i) the time-dependent heat-transfer coefficient at the surface of a steel rod which has been water-cooled after induction heating (non-stationary situation) ; ii) the space-dependent heat flow at the surface of a direct chill cast aluminium slab (stationary situation) ; and iii) the temperature-dependent thermal conductivity of aluminium-silicon alloys. In this latter case, the influence of the silicon concentration on the thermal conductivity is clearly revealed.