The pyrolysis of particles of coal (or biomass), small enough for internal conduction of heat not to be a controlling factor, is considered. Altogether five dimensionless groups are identified as characterising both the rates of pyrolysis and the change in temperature of these small isothermal particles. A sensitivity analysis demonstrates that three dimensionless groups easily have most influence on the kinetics of pyrolysis. This enables a simple mathematical model to be formulated, but assuming that only one reaction for thermal decomposition occurs at a time. The heat of devolatilisation is not ignored. It is found that, if the temperature around such a pyrolysing particle exceeds a threshold value, external heat transfer controls the rate of pyrolysis. In fact, whether there is kinetic or external heat transfer control is mainly determined by the two dimensionless groups 3Nuk(l.infinity)/2A rho c,o (C) over barr(0)(2) (a modification of the ratio of the characteristic times for chemical reaction and a coal particle to heat up) and RT,.IE,. Thus, for kinetic control RT infinity/E-v must be smaller than a critical value, i.e. E, has to exceed a threshold value. The third important group, R Delta H-v/(C) over bar CEv, has less influence. Under kinetic control, a particle's temperature is close to the ambient temperature and consequently does not change during thermal decomposition, whereas, when external heat transfer controls, the particle's temperature can rise during pyrolysis by up to 100 K. The mean value of the activation energy for the devolatilisation of many coals is deduced to be approximate to 240 kJ/ mol, i.e. higher than many measured values, which appear to have been obtained, when heat transfer controlled the rate. The temperature during pyrolysis of these "thermally thin particles" is not altered significantly by fragmentation, swelling or a change of shape. (C) 2009 The Combustion Institute. Published by Elsevier Inc. All rights reserved.