Thermal energy transport across the interfaces of physically and chemically modified graphene with two metals, Al and Cu, was investigated by measuring thermal conductance using the time-domain thermoreflectance method. Graphene was processed using a He2+ ion-beam with a Gaussian distribution or by exposure to ultraviolet/O3, which generates structural or chemical disorder, respectively. Hereby, we could monitor changes in the thermal conductance in response to varying degrees of disorder. We find that the measured conductance increases as the density of the physical disorder increases, but undergoes an abrupt modulation with increasing degrees of chemical modification, which decreases at first and then increases considerably. Moreover, we find that the conductance varies inverse proportionally to the average distance between the structural defects in the graphene, implying a strong in-plane influence of phonon kinetics on interfacial heat flow. We attribute the bimodal results to an interplay between the distinct effects on graphene’s vibrational modes exerted by graphene modification and by the scattering of modes.