The preform-to-fiber thermal drawing process has been recently proposed for the fabrication of fibers and microchannels with submicrometer surface textures. To better control the final architecture and reach small feature size down to tens of nanometers however, a proper understanding and modeling of the fluids dynamics at play during the fabrication of the texture is needed. Here, we present an analytical model describing comprehensively the reflow of periodic polymer micropatterns of arbitrary shape in isothermal annealing as well as in a fiber drawing process. Experiments on square-grooved thermoplastic plates subjected to both treatments show excellent agreement with the calculated theoretical values. Based on this model, we could identify a strategy and the corresponding materials to fabricate sub-100 nm surface-patterned fibers. These results deepen the understanding and control of thermal-based approaches for polymer surface texturing and open novel opportunities for textured fibers and microchannels in bioengineering, microfluidics, or smart textiles. Published under license by AIP Publishing.