A mixture of waste-wood biomass and municipal biosolids waste was composted in a plastic container inside of an insulated chamber. The mixture of biomass and biosolids was approximately 50:50 and weighed 82.6 kg. The peak temperature of the compost was 32.4◦C. The small scale of the compost system allowed the lower limit of the compost decomposition rate to be studied. A model was successfully developed to predict the core temperature of the compost using the ambient temperature in the insulated chamber. A literature review was conducted to determine literature values for the overall convective and conductive heat transfer coefficient, the dry mass fraction, and heat of combustion for both biomass and biosolids. The model used an optimization algorithm to calculate the rate constant for the experimental setup. The calculated decomposition rate constant was 0.0525 Day−1.