Direct contact melting process takes place in a lot of technological processes. One of the important applications is in the thermal storage system. In this system, phase change material is stored in small spherical capsules. Diameter of the capsule is about 4 inches. Millions of capsules are packed in a thermal storage tank. Capsules are heated and cooled through brine. Direct contact takes place in the melting process of the thermal storage system. In this system, latent heat energy is used effectively. This paper presents a theoretical study of the direct contact melting process on a spherical heating wall that has arbitrary temperature distribution. Governing system of equations with heat convection terms is solved analytically. It is shown that it can be transformed into ordinary differential equations system by a similarity transformation. Temperature is solved using perturbation method. This solution is valid for almost all practical Stefan number. Analytical solution is obtained for a typical temperature distribution. It is shown that melting rate is enhanced by more than 10% by the effect of temperature distribution.