In fused filament fabrication (FFF), it is important to know the time required for a pair of cylinders to coalesce and form a single cylinder. Virtually all present day mathematical models for sintering of polymer particles are based on Frenkel's model, which was originally developed for the start of the coalescence. It is based on the assumption that the process time is determined by the balance of surface tension and viscous forces. The original model and subsequent modification, by the first author and coworkers, was for two spherical particles. In sintering of spheres the balance is carried out for a biaxial flow field. For cylinder sintering the flow field is planar. Frenkel's model has been modified for planar flow and extended to the completion of the process. Heat transfer effects have also been taken into consideration, through the viscosity dependence on temperature. Dependence of surface tension on temperature, could have been easily included, but it was not taken into consideration because the viscosity dependence is one order of magnitude larger.Comparisons were made to an isothermal model presented by Hopper, where an inverse ellipse shape was used to describe the evolving geometry, rather that two intersecting cylinders of the present case.Comparison with some experimental data has also been carried out.