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In this work the differential Friedmann-Lemaître-RobertsonWalker model solutions which offer different cosmological parameters. We studied the effect of time and temperature evolution on these cosmological parameters, such as the scale factor R(t) and the deceleration parameter q, across radiation, matter and dark energy eras. The nature of the variations in time and temperature of these quantities are consistent with that obtained from other cosmological models which have taken into account astrophysical observations. Time and temperature variations of these parameters have been shown graphically. These parameters provided strong evidence about the expansion and acceleration of the universe. The scale factor and the deceleration parameter show a linear change with the increase in time during the radiation and matter dominated eras, followed by a rapid expansion during the dark energy era, indicating that the universe has a transition from a phase of decelerated expansion to an accelerated expansion, which is contributed to dark energy. This led to a flat, homogeneous, and isotropic universe.

Variation of Scale Factor and Deceleration Parameter Through the Cosmic Evolution of Time and Temperature