An illustrative example embodiment of a method of making a concrete expansion joint insert includes moving a material including a resin having a melt temperature through a die having a flow passage that ends in an exit having a selected geometry, increasing a temperature of only a segment of the die near the exit to an elevated temperature that is at least 1.5 times the melt temperature, and increasing the temperature of a portion of the material to an increased temperature above the melt temperature through contact with the segment having the elevated temperature.