We investigate the creation of dark matter particles as a result of the decay of the scalar field in the framework of warm inflationary models, by using the irreversible thermodynamics of open systems with matter creation/annihilation. We consider the scalar fields, radiation and dark matter as an interacting three component cosmological fluid in a homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker (FLRW) Universe, in the presence of the curvature terms. The thermodynamics of open systems
as applied together with the gravitational field equations to the three component cosmological fluid leads to a generalization of the elementary scalar field-radiation interaction model, which is the theoretical basis of warm inflationary models. Moreover, the decay (creation) pressures describing matter production are explicitly considered as parts of the cosmological fluid energy-momentum tensor. A specific theoretical model, describing coherently oscillating scalar waves, is considered. In particular, we investigate the role of the curvature terms in the dynamical evolution of the early Universe, by considering numerical solutions of the gravitational field equations. Our results indicate that despite the fact that the Universe becomes flat at the end of the inflationary era, the curvature terms, if present, may still play an important role in the very first stages of the evolution of the Universe.