The structure of Bunsen cone flame tops is studied using the thermal diffusion flame model. Assuming a strong temperature dependence of the reaction rate, the shape of the flame front as well as the temperature distribution at the front are found. It is shown that for the case in which the Lewis number of the limiting component is greater than unity, the front is a smooth surface with a radius of curvature at the flame top substantially exceeding the width of the preheating zone. Towards the flame top, the temperature in the reaction zone increases along with the velocity of the flame relative to the gas. When the Lewis number of the limiting component is less than unity, the temperature at the front decreases towards the flame top, the velocity of the flame relative to the gas drops, and the flame is extinguished at distances close to the top.