One of the major limitations of fused deposition modeling (FDM) is part strength of the products, due to the weak strength between fibers (bond strength). This work describes the process parameters that affect bond strength, and the theories describing it. Four-sided ABS boxes with a wall thickness equal to a single fiber width were printed according to a design of experiments. A set of tensile specimens were cut from the printed box and tested in the fiber and cross-fiber directions: smaller layer thicknesses, larger fiber widths, faster print speeds, and higher nozzle and platform temperatures increased interlayer bond strength. Modeling was conducted to understand the underlying mechanisms. Reptation time governs the diffusion of polymer chains across the fiber interfaces, so the frequency response of the ABS was characterized to measure the reptation time at multiple temperatures. A one-dimensional transient heat analysis provided an estimate of the temperature profile of the interface between layers. By transposing temperature-dependent diffusion coefficients onto the interface temperature profiles, the amount of polymer chain diffusion that occurred across the layers was calculated for all the tested processing conditions. Bond strength versus total diffusion was found to match well with polymer healing models, showing that the healing models developed for polymer welding can be applied to the non-isothermal FDM process. The findings support that diffusion, wetting, and intimate contact all separately affected bond strength. Fundamental models for predicting FDM part strength should, therefore, consider all three of these factors. This study provides processing recommendations for producing the strongest FDM parts. These recommendations can be useful for companies producing FDM products as well as companies designing printers. With the correct processing conditions, the strength limitations from FDM can nearly be eliminated.