Abstract-Inverse Heat Conduction Problems(IHCPs) have been extensi vely studied over the last 60 years. They have numerous applications in many branches of science and technol ogy.The problem consists in determining the temperature and heat flux at inaccessible parts of the boundary of a 2-or 3-di mension al body from correspondi ng data-called " Cauchy data" on accessible parts of the boundary. It is well-known that IHCPs are severely ill-posed which means that small perturbations in the data may cause extremely large errors in the soluti on. In this contri buti on, I present an anal ysis of numerical soluti on of nonlinear inverse heat conduction problem in a region wi th movi ng boundaries, a regul arizati on method is used to construct an algorithm for smoothing the experi mental data in a complication of the input data for the i nverse problem.