A numerical analysis of thermal stress over temperature variations near the crystal-melt interface is carried out for a floating-zone growth of Cadmium Telluride (CdTe). Thermocapillary convection determines crystal-melt interfacial shape and signature of temperature in the crystal. Large temperature gradients near the crystal-melt interface yield excessive thermal stresses in a crystal, which affect the dislocations of the crystal. Based on the assumption that the crystal is elastic and isotropic, thermal stresses in a crystal are computed and the effects of operating conditions are investigated. The results show that the extreme thermal stresses are concentrated near the interface of a crystal and the radial and the tangential stresses are the dominant ones. Concentrated heating profile increases the stresses within the crystal, otherwise, the pulling rate decreases the stresses.