One of the important parameters in cosmology is the parameter characterizing the equation of state (EOS) of the sources driving the cosmic expansion. Epochs that are dominated by radiation, matter or scalar fields, whether they are probed either directly or indirectly, can be characterised by a unique value of this parameter. However, the EOS parameter during reheating - a phase succeeding inflation which is supposed to rapidly defrost our Universe - remains to be understood satisfactorily. In order to circumvent the complexity of defining an instantaneous EOS parameter during reheating, an effective parameter weff, which is an average of the EOS parameter over the duration of reheating, is usually considered. The value of weff is often chosen arbitrarily to lie in the range -1/3=weff=1. In this work, we consider the time evolution of the EOS parameter during reheating and relate it to inflationary potentials V(f) that behave as fp around the minimum, a proposal which can be applied to a wide class of inflationary models. We find that, given the index p, the effective EOS parameter weff is determined uniquely. We discuss the corresponding effects on the reheating temperature and its implications. © 2020 American Physical Society.