Identifying the forces that drive a phase transition is always challenging. The hcp-fcc phase transition that occurs in cobalt at ~700 K has not yet been fully understood, although early theoretical studies have suggested that magnetism plays a main role in the stabilization of the fcc phase at high temperatures. Here, we perform a first principles study of the free energies of these two phases, which we break into contributions arising from the vibration of the lattice, electronic and magnetic systems and volume expansion. Our analysis of the energy of the phases shows that magnetic effects alone cannot drive the fcc-hcp transition in Co and that the largest contribution to the stabilization of the fcc phase comes from the vibration of the ionic lattice. By including all the contributions to the free energy considered here we obtain a theoretical transition temperature of 825 K.