In this article, the ghost fluid-lattice Boltzmann method, used to simulate the curved boundaries is combined with an extrapolation based refilling method to cope with the moving curved boundaries, where in each iteration some of the solid nodes step into the fluid domain. The refilling method is used to approximate the unknown density and internal energy distribution functions of such solid nodes. To examine the accuracy of the presented method, several case studies are considered. From those case studies, natural convection problem between to concentric and eccentric cylinders as well as heat transfer from a cylinder in a cross flow are considered to validate the ghost-fluid lattice Boltzmann method used to simulate the hydrodynamic and thermal conditions at the curved boundaries. To test the accuracy of the employed refilling method, sedimentation of a single isothermal cold particle in a vertical channel investigated. The results show that the presented ghost fluid-lattice Boltzmann method with refilling is capable of simulating the moving thermal curved boundaries with excellent accuracy.