Stresses result when polymer feed stock is extruded through the nozzle of a three-dimensional (3D) printer, causing undesirable surface roughness called “sharkskin,” which hinders effective bonding to the substrate. A promising method to remove the sharkskin is to reheat the polymer after extrusion. However, questions remain about the appropriate design parameters to guarantee success. A mathematical model is presented for this system, and both amorphous and crystalline polymers are examined. The former is a heat transfer problem; the latter a Stefan problem. Several effectiveness conditions are considered, including exit temperature and a duration condition related to the polymer relaxation time. Our results provide guidance on designing effective postextrusion heaters.