The problems of heat conduction resulting from a moving heat source applies to many fields of engineering such as welding, surface hardening, moving friction between mechanical parts, laser treatments etc. Heat source models are used to define the heat flux distribution in the domain.An attempt has been made to gather the information about moving heat source problems and different heat source models. The optimal design reduces failure rates, improves product life cycle and important to all it will find out defects due to temperature distribution within the material. The analytical solutions are available for simple problems but as the complexicity increases the analytical solutions fail to predict results. Numerical method is a key to solve many complicated mathematical problems.