This study investigates the effects of adding the area and curvature terms to the volume term in the quark and gluon density of states on the transition temperature, at which the deconfinement phase transition occurs. The analysis begins with the computation of the partition function of both the Hadronic Gas (HG) and the Quark–Gluon Plasma (QGP) projected onto the SU(3) color-singlet representation, using the projection method, within the quark and gluon density of states given by the Multiple Reflexion Expansion (MRE) approximation. We consider the transition between a Hadronic Gas (HG) phase, consisting of massive pions, and a Quark–Gluon Plasma (QGP) phase, which includes gluons, massless up and down quarks, and massive strange quarks along with their antiquarks, in the framework of the Bag model and the phase coexistence model. We then examine the variations in the pressure of both the Hadronic Gas (HG) and the Quark–Gluon Plasma (QGP) phases, with the aim of determining the transition temperature in different cases of contributing terms in the quark and gluon density of states: considering the contributions of the volume term only, volume and area terms, volume and curvature terms, and the combination of the three volume, area and curvature terms.