This thesis explores the roles of physical and mathematical modelling in the prediction of temperature profiles in the composting process. A literature-based evaluation of the performance of laboratory- and pilot scale composting reactors, showed that physical models used in composting research frequently do not properly simulate the full-scale composting environment, and may therefore produce results which are not applicable at full scale. In particular, self-heating, laboratory-scale, reactors typically involve significant convective/conductive/radiative losses, even with insulation present. This problem can be overcome by using controlled temperature difference or controlled heat flux laboratory reactors, which allow convective/conductive/radiative heat fluxes to be controlled to levels close to those occurring in full-scale systems. A new method of assessing the simulation performance of composting systems is presented. This utilises the areas bounded by the temperature-time profile and reference temperatures of 40 and 55 ℃ (A₄₀ and A₅₅), the times for which these temperatures are exceeded (t₄₀ and t₅₅), and times to peak temperature. An evaluation of published temperature profiles showed a marked difference in these parameters when comparing many laboratory- and full-scale reactors. The impact of aeration is illustrated, and laboratory- and pilot-scale reactors able to provide good temperature profile simulation, both qualitatively and quantitatively, are identified. Mathematical models of the composting process are reviewed and their ability to predict temperature profiles assessed. The most successful models in predicting temperature profiles have incorporated either empirical kinetic expressions, or utilised a first-order model, with empirical corrections for temperature and moisture. However, no temperature models have been able to predict maximum, average and peak temperatures to within 5, 2 and 2 ℃ respectively, or to predict the times to reach peak temperatures to within 8 h, although many models were able to successfully predict temperature profile shape characteristics. An evaluation of published constant-temperature and varying-temperature substrate degradation profiles revealed very limited evidence to support the application of single exponential, double exponential or non-logarithmic Gompertz functions in modelling substrate degradation kinetics, and this was identified as a potential weakness in the temperature prediction model. A new procedure for correcting substrate degradation profiles generated at varying temperature to a constant temperature of 40 ℃ was developed and applied in this analysis, and on experimental data generated in the present work. A new approach to the estimation of substrate degradation profiles in the composting process, based on a re-arrangement of the heat balance around a reactor, was developed, and implemented with both a simulated data set, and data from composting experiments conducted in a laboratory-scale constant temperature difference (CTD) reactor. A new simulated composting feedstock for use in these experiments was prepared from ostrich feed pellets, office paper, finished compost and woodchips. The new modelling approach successfully predicted the generic shape of experimental substrate degradation profiles obtained from CO2 measurements, but under the conditions and assumptions of the experiment, the profiles were quantitatively different. Both measured CO2-carbon (CO2-C) and predicted biodegradable volatile solids carbon (BVS-C) profiles were moderately to well fitted by single exponential functions with similar rate coefficients. When corrected to a constant temperature of 40 ℃, these profiles gave either multi-phase or double exponential profiles, depending upon the cardinal temperatures used in the temperature correction procedure. If it is assumed that the double exponential model generated is correct, this work provides strong evidence that a substrate degradation curve generated under appropriate laboratory conditions at 40 ℃ would, given the correct cardinal temperatures, generate a correct substrate degradation profile under varying temperature conditions, and that this in turn would enable an accurate and precise prediction of the temperature profile using a heat and mass balance approach. This finding opens the door for the development of a simple laboratory test for composting raw material characterisation, but underlines the need for accurate estimates of the physical cardinal temperatures. Experimental factors appear to be the likely cause of the dysfunction between previously reported substrate degradation patterns and existing substrate degradation models, and suggestions for further research are provided in order to more precisely and accurately quantify these factors.