variavel0=Sandro Metrevelle Marcondes Lima e Silva - metrevel@mecanica.ufu.br Universidade Federal de Uberlandia Valério Luiz Borges - vlborges@mecanica.ufu.br Universidade Federal de Uberlândia Louriel Oliveira Vilarinho - L.Vilarinho.2001@Cranfield.ac.uk Universidade Federal de Uberlândia Américo Scotti - ascotti@mecanica.ufu.br Universidade Federal de Uberlândia Gilmar Guimarăes - gguima@mecanica.ufu.br Universidade Federal de Uberlândia Abstract. The heat input measurement during the welding process is a high-complex task. The main reason is due to the fact that welding arc is a non-uniform heat source. To solve this problem, some analytical and numerical approaches have been proposed. They are divided up two categories, direct and inverse problem of heat transfer. One problem is considered direct when the boundary conditions are prescribed for the outside surface of the domain. In a inverse problem, information concerning one or more boundary conditions are unknown. Thus, a inverse problem requires the temperature knowledge in one determined inside point of the domain, in order to obtain the temperature profile on the unknown surface. In this work, a methodology is proposed to calculate the heat amount delivered to the workpiece during the welding process. In this case, the inverse problem technique is based on the conjugated gradient method with adjoint problem. The theoretical model was built from the diffusion equation over a plate. On the opposite of known models that consider a bidimensional plate with relative speed equal to the heat source, the proposed model considers a tridimensional heat transfer with spatial and temporal heat source variation. To assess the proposed technique, different welding conditions were used during TIG process. The arc heat input was estimated through the temperature measurement in the opposite surface of the weld bead, using ten thermocouples equally spaced on the medium line plate. Keywords. Inverse Problems, Heat Conduction, Conjugate Gradient, Optimization, GTA Welding Process.