In our earlier work (S.E. Bechtel et al., J Appl Mech 2000;67(1):197-206) we created a model for slip of linearly elastic belts on pulleys, and adapted our model to isothermal draw of fibers on rollers (submitted for publication). Here, we. (i) incorporate temperature dependence, (ii) extend the constitutive characterization to piecewise linearly elastic-plastic fibers to capture the softening behavior of as-spun fibers, and (iii) assemble governing equations for fibers on rollers and in freespans, together with matching conditions, to produce a comprehensive model for a two-stage, non-isothermal industrial draw process. The model is then employed to simulate three representative drawlines.