The thermal stress produces in a single crystal during fiber growth by temperature variations is analytically obtained and numerically calculated for various Biot numbers and interface shape of the melt and the solid. It is found that maximum stress and dislocation density were produced during the single crystal growth for the growing interface concaving towards the melt with a large Biot number. The temperature distribution far beyond the interface shows little or no difference between the convexed and concaved conditions along the axial and radial direction. However, it is shown that single crystals at the periphery and tip of the concaved‐ interface have thermal stress (dislocation) 4.8 times higher than the ones with the convexed‐interface. The thermal stresses or dislocation density of the spinel calculated from the optical micrograph photographs have the same trends as the derived model.