The Grüneisen parameter is an important parameter for the thermal state and evolution of the core, but its uncertainties and their implications are sometimes overlooked. Several formalisms using different parameters values have been used in different studies, making comparison between studies difficult. In this paper, we use previously published data sets to test the sensitivity of modelling the thermal state of the early core to the different formalisms and parameter values used to describe the evolution of the Grüneisen parameter with density. The temperature of the core obtained in our models is less sensitive to the uncertainties of the parameters used in Al'Tshuler et al. formalism than the uncertainties of the parameters used in Anderson formalism.