•Kinetic conditions have been compared in dry anaerobic digestion of complex wastes.•The condition evaluated has been the temperature, exactly, mesophilic (35°C) and thermophilic (55°C) range.•Important kinetic differences are showed between both processes, even though of complex wastes.•The conclusions may help to increase the efficiency in dry anaerobic process at industrial scale. Temperature is a significant variable in anaerobic digestion (AD) since it determines the values of the main kinetic parameters for the process and, hence, the rate of the microbiological process. Thus, in this study, batch AD experiments were carried out, at mesophilic (35°C) and thermophilic (55°C) conditions, with the aim to compare the kinetic of both processes. Tests were performed in dry conditions (concentration of Total Solids (TSs) of 20%) using the Organic Fraction of Municipal Solid Waste (OFMSW) as feedstock. Romero model 1 was used to fit the experimental results from both, the organic matter consumption and the biogas production. This model has been used extensively in the analysis of results of AD process in a wide range of experimental conditions 2–4. The values of the maximum specific growth rate of microorganisms (μMAX) are 27–60% higher for thermophilic process than for mesophilic ones and, therefore, the same level of organic matter degradation and methane production can be achieved in a shorter operating time, 20days in thermophilic instead of 40days in mesophilic. Moreover, the yield coefficient for methane production (αP/S) and the initial amount of active microorganisms (XV0/YX/S) show values 107% and 129% higher, respectively, in thermophilic processes.