The present study investigated the influence of pressure on the thermal effects associated with the pyrolysis of biomass macrocomponents: cellulose, hemicellulose, and lignin. The heat demand of the pyrolysis process was measured by differential scanning calorimetry at pressures ranging from 0.1 to 4 MPa, using a specifically developed experimental configuration. An increase of the operating pressure affected both the heat demand and the final char yield. A summative model to describe the overall heat demand of the pyrolysis process was tested, and the results were compared to those obtained for an actual biomass sample and a mixture of cellulose, xylan, and lignin (synthetic biomass). Both samples showed important differences in the thermal demand with respect to that obtained from the summative model, possibly because of interactions among volatiles generated in the pyrolysis process and differences in the amounts of ash and extractives present in the samples.