Simplified equations for the cooling time of glass fibers to the solid state are deduced from the theory of heat conduction. The approximations made are based upon a value of the order of 1 for Nusselt's number. This value ofNuholds for comparable metallic fibers, as measured by Mueller, and is assumed to hold for glass fibers. The relation of pulling speed and flow rate to cooling time is shown. Calculations of cooling time of typical small glass fibers show that they are of the same order as the Maxwell relaxation time of the glass at roughly 900°C. The consequence of this correlation is discussed in terms of the high strength of fibers, and the high ``fictive'' temperature of fibers.