The interaction between graphene and metals represents an important issue for the large-area preparation of graphene, graphene transfer and the contact quality in graphene devices. We demonstrate a simple method for estimating and manipulating the level of interaction between graphene and copper single crystals through heat treatment, at temperatures from 298K to 1073K. We performed an in-situ Raman spectroscopy showing Cu face-specific behavior of the overlying graphene during the heat treatment. On Cu(111) the interaction is consistent with theoretical predictions and remains stable, whereas on Cu(100) and Cu(110), the initially very weak interaction and charge transfer can be tuned by heating. Our results also suggest that graphene grown on Cu(100) and Cu(110) is detached from the copper substrate, thereby possibly enabling an easier graphene transfer process as compared to Cu (111).