A model for estimation of the profiles of erosion and buildup material in the hearth of an ironmaking blast furnace has been developed. The model is based on thermocouple readings in the hearth wall and bottom and solves an inverse heat transfer problem for two-dimensional slices of the hearth geometry to estimate the inner profile. Special attention has been paid to the mathematical formulation of the problem at hand, yielding a general model optimized for fast computation. This includes a flexible formulation of the boundary condition a generic setup of the lining materials applied in the hearth refractory, and a sophisticated iterative procedure ill the estimation of the location of the internal profile. These steps have led to a model that facilitates process analysis with estimation and reestimation of the furnace hearth conditions over whole campaigns using different parameter settings. The model has been applied to study the evolution of the hearth erosion and buildup formation processes in several industrial furnaces.