The transient heating of a polymer preform within a cylindrical furnace is the initial step in the manufacture of polymer optical fiber. A numerical model was used to simulate the radiative and convective heat transfer within the furnace enclosure during this initial heating. Results illustrate a strong dependence of the preform’s heating rate on the radiative properties of the preform. Due to the prominence of radiative heat transfer at steady-state, the resulting axial temperature profile within the preform is strongly coupled to the corresponding axial temperature profile of the furnace wall. Numerical predictions were compared with experimental results for several preform surface emissivities, preform diameters, and thermal boundary conditions. The results compare well for preforms with well-characterized surface finishes (such as black paint and aluminum), with discrepancies between experimental and numerical results typically less than 1.3°C. Experiments indicate that the heating characteristics of poly(methyl methacrylate) preforms can be adequately simulated by assuming that the preform exhibits nearly blackbody behavior (ε = 0.96) when exposed to the low furnace temperatures (85°C) used in this study. Finally, the experiments revealed the tendency for unstable natural convection within tall furnace cavities, with experimental readings indicating oscillatory air temperatures as the system approached steady-state.