In the five-dimensional Einstein gravity, the simplest chaotic inflationary scenario on a 3-brane universe in a bulk space–time undergoes significant corrections, when the five-dimensional Planck scale is below about 1017 GeV. As well as, the non-minimal coupling between the inflaton field and the induced scalar curvature on the Randall–Sundrum (RS) II brane leads to considerable modifications of the Friedmann constraint equation that affect on the inflationary dynamics of this braneworld model. In this paper, we revisit the main perturbation parameters in these two modified models with some sort of polynomial potentials in the reheating phase and perform a numerical analysis on the parameter space of the adopted models in confrontation with Planck 2018 data. There is no observational evidence to directly detect the reheating phase, but it could be parameterized in terms of the reheating final temperature Tre, a number of e-folds during reheating Nre and effective equation of state parameter during reheating, ωre, which make a useful bridge between the reheating and inflationary eras. We obtain several significant constraints on the two inflationary braneworld models for some values of the parameter ωre. The finite range of effective equation of state parameter in reheating era gives explicit constraints on the tensor-to-scalar ratio, r and the number of e-folds, Nk. Therefore, in the next step we obtain some allowed ranges of the reheating equation of state parameter from acceptable subspaces in the Nre −ωre phase plane in confrontation with Planck 2018 data. The comparison of these constraints for two different values of the brane tension as λ = 105 and λ = 109 in appropriate units, specifies the brane tension’s role in reheating stage after minimal inflation on the brane. Then, we obtain such constraints from reheating phase in a non-minimal inflationary model on the RS II brane with induced gravity. Finally, we compare the reheating constraints in these two mini
