The recent novel temperature-modulated differential scanning calorimetry (TA Instruments MDSC TM) technique has been applied to the measurement of thermal properties of GexAsyS60 chalcogenide glasses in the glass transition region in bulk glasses and in their thin films. The reversing and non-reversing heat flows through the glass transformation region during both heating and cooling schedules were measured and the values of the parameters, T-g, Delta H, C-p and Delta C-p, which characterize the thermal events in the glass transition region, were determined. The structurally determined parameters, T-g, Delta H, C-p and Delta C-p, reveal significant changes with composition because in the GexAsyS60 glasses the average coordination number, [r], increases from 2.4 to 2.8 with increasing x from 0 to 40 at % Ge. A maximum in T-g, Delta H and C-p and a minimum in the heat capacity change, Delta C-p, at T-g occur near the composition for which x approximate to 30 at% Ge. These extrema which appear in both films and bulk glasses are ascribed to a change in the network function of Ge atoms replacing As atoms in a covalent network. Recent structural models for chalcogenide glasses have been considered to explain the observed thermal properties.