Interest in biogas has increased due to natural gas shortages and the energy transition. Most digesters in the EU have internal heating for process stability. Unheated reactors could potentially lower costs, but have decreased kinetics due to low operational temperatures, especially in winter. This raises the question how seasonal temperature fluctuations effect biogas production. If this effect could be incorporated in current models such as the Anaerobic Digestion Model no.1 (ADM1), scenarios could be compared to investigate when heating is worthwile. In this thesis, an extension is created to the ADM1 in Python to predict the operational temperature and its effects on the anaerobic digestion process. To lower the stiffness of the ADM1, different pH calculation methods were compared. These methods and the used Python version of the model were validated by digestion of the Benchmark Simulation Model 2 (BSM2) ADM1 influent. It was found that the combination of the Differential Algebraic Equation (DAE) with the Radau numerical solving method produced the smallest errors with the lowest computational burden. A heat-transfer model was included, which calculates bulk liquid temperature as a function of weather data, digester design and some operational factors. A One-At-a-Time (OAT) sensitivity analysis showed the dependence of yearly temperature fluctuations on several design and operational parameters. The calculated operational temperature is coupled to the ADM1 through several temperature inhibition functions for biochemical processes. Furthermore, the dependency of the liquid-gas transfer coefficient was investigated. It was found that this last step in biogas production could potentially become rate-limiting at temperatures lower than 30 °C, but this result was not validated. The coupled heat transfer - ADM1 model is used to study the case of an unheated fixed-dome reactor for the co-digestion of spent wort and Waste Activated Sludge (WAS) of the La Trappe brewery in the Netherlands. The influent substrate concentrations were determined by a biochemical fractionation procedure, and the model was able to simulate methane production curves found in Biochemical Methane Potential (BMP) experiments. Simulations of digestion for the La Trappe case showed seasonality in biogas production, increasing in summer and decreasing in winter. The extent of the effect was found to be dependent on substrate composition, with lipid-rich substrates being affected more than carbohydrate- or protein-rich substrates. Furthermore, the simulation showed seasonality in rate limiting step, with hydrolysis in summer and methanogenesis in winter. This caused the pH to lower with winter, and it was found that higher base dosage is needed in colder winters to prevent acidification. Higher influent temperatures improved process stability, lowered amounts of base needed and increased biogas production. Furthermore, the relation between temperature and volume showed that washout of methanogens and consequent VFA accumulation is dependent on the absolute temperature inhibition function for acetoclastic methanogens. Simulation of the digestion of BSM2 influent showed that the maximum Organic Loading Rate (OLR) increased with temperature till 30 °C, but decreased above this point as free ammonia inhibition starts to limit methanogenic metabolism. For La Trappe, OLR determines the needed base dosage, allowing smaller volumes if more base is added. Lastly, internal heating with the produced biogas was investigated, and optimal heating for biogas production was found. The found results from the model were used to asses the costs and benefits of several design and operational options for the digester at La Trappe. This digester will be used in future research for validation of the model.