Knowledge about the curing behavior of a thermosetting resin and its composites includes the determination of kinetic parameters and constitutes an important scientific and technological tool for industrial process optimization. In the present work, the differential scanning calorimetry (DSC) technique was used to determine several curing parameters for pure epoxy and its composite reinforced with 20 vol % mallow fibers. Analyses were performed with heating rates of 5, 7.5, and 10 °C/min, as per the ASTM E698 standard. The kinetic related parameters, that is, activation energy (E), Avrami’s pre-exponential factor (Z), and mean time to reach 50% cure (t½), were obtained for the materials, at temperatures ranging from 25 to 100 °C. Response surfaces based on the mathematical relationship between reaction time, transformed fraction, and temperature were provided for optimization purposes. The results showed that the average curing time used for the production of diglycidyl ether of bisphenol A/triethylenetetramine (DGEBA/TETA) epoxy systems or their composites reinforced with natural mallow fibers can be considerably reduced as the temperature is increased up to a certain limit.