The process creates a radial temperature gradient in an extruded strand in a direction normal to the direction of motion thereof (that is, normal to the longitudinal direction thereof) so that upon exiting the first quench region the surface of the strand has solidified while at least the preponderant portion of the interior of the strand remains above the cold crystallization temperature, Tcc Then, in the annealing region, heat from the warmer interior will be transferred to the cooler surface, causing the surface to heat up into the range of Tcc, thereby inducing the surface to undergo crystallization. Once the surface has undergone crystallization, the strand is thoroughly quenched in a second quench region so that the strand will be ready for pelletization, accumulation or other handling steps.