This thesis addresses two similar problems that combine the theory of Coulomb drag with the emerging field of graphene physics. First, the theory of Coulomb drag between two graphene mono-layers is extended to include finite temperature. It is found that the effect is strongly enhanced at intermediate temperatures by coupled plasmon modes. This behaviour is similar to that seen between two dimensional electron gasses. In the second, we investigate the finite temperature polarisability of a graphene bilayer and apply this to the problem of Coulomb drag in a bilayer system. We find that enhancement due to coupled plasmon nodes is suppressed, and dependence of the position and width of the plasmon peak on carrier density and interlayer separation is enhanced.