This article shows the estimation of a 2D heat transfer coefficient. The study is a continuation of our previous investigations [P. Le Masson, D. Carron, P. Rogeon and J.J. Quemener (1999). Identification du coefficient de transfert lors d'un essai Jominy instrumenté. SFT, 99, 57-62; P. Le Masson, T. Loulou, E. Artioukhine, P. Rogeon, D. Carron and J.J. Quemener (2001). A new approach for the estimation of a convection heat transfer coefficient during a "metallurgical Jominy end-quench " test. 68th Eurotherm Seminar. Poitiers, France.]. A cylindrical steel bar (L = 100 mm and d = 25 mm) is heated up to 900°C and then quenched by a water jet sprayed on its lower end. The problem under analysis is multifaceted. First, during the exchange phase between water and solid surface, phenomena like vaporization, boiling or forced convection occur. Second, the metallurgical phase changes of the considered material have to be taken into account in the examination of the heat treatment problem. The study is conducted to examine and to solve a nonlinear thermo-metallurgical inverse problem of estimating time and space dependent convection heat transfer coefficient. In a first part, we compare two methods for estimating this 2D heat transfer coefficient: the Iterative Regularization Method "IRM" [O.M. Alifanov, E.A. Artyukhin and S.V. Rumyantsev (1995). Extreme Methods for Solving III-posed Problems with Applications to inverse Heat Transfer Problems. Begell House, N-Y.] and the Function Specification Method "FSM" with a spatial regularization [J.V. Beck, B. Blackwell and C.R. St Clair (1985). Inverse Heat Conduction Ill Posed Problem. Wiley, New York.]. In a second part, we show an experimental estimation of the 2D heat transfer coefficient with the Iterative Regularization Method.