A long-term comparative study using continuously-stirred anaerobic digesters (CSADs) operated at mesophilic and thermophilic temperatures was conducted to evaluate the influence of the organic loading rate (OLR) and chemical composition on process performance and stability. Cow manure was co-digested with dog food, a model substrate to simulate a generic, multi-component food-like waste and to produce non-substrate specific, composition-based results. Cow manure and dog food were mixed at a lower - and an upper co-digestion ratio to produce a low-fiber, high-strength substrate, and a more recalcitrant, lower-strength substrate, respectively. Three increasing OLRs were evaluated by decreasing the CSADs hydraulic retention time (HRT) from 20 to 10 days. At longer HRTs and lower manure-to-dog food ratio, the thermophilic CSAD was not stable and eventually failed as a result of long-chain fatty acid (LCFA) accumulation/degradation, which was triggered by the compounded effects of temperature on reaction rates, mixing intensity, and physical state of LCFAs. At shorter HRTs and upper manure-to-dog food ratio, the thermophilic CSAD marginally outperformed the biomethane production rates and substrate stabilization of the mesophilic CSAD. The increased fiber content relative to lipids at upper manure-to-dog food ratios improved the stability and performance of the thermophilic process by decreasing the concentration of LCFAs in solution, likely adsorbed onto the manure fibers. Overall, results of this study show that stability of the thermophilic co-digestion process is highly dependent on the influent substrate composition, and particularly for this study, on the proportion of manure to lipids in the influent stream. In contrast, mesophilic co-digestion provided a more robust and stable process regardless of the influent composition, only with marginally lower biomethane production rates (i.e., 7%) for HRTs as short as 10 days (OLR = 3 g VS/L-d).