Materials science has made progress in maximizing or minimizing the thermal conductivity of materials, however, the thermal effusivity – related to the product of conductivity and capacity – has received limited attention, despite its importance in the coupling of thermal energy to the environment. We design materials that maximize the thermal effusivity by impregnating high surface area copper (Cu) and nickel (Ni) foams with conformal chemical vapor deposited graphene (G) and octadecane (OD) as a phase change material, achieving values exceeding J m-2 (s K)-1/2 – the highest value in the literature, to date, for isotropic, ambient phase change materials. The graphene is shown to increase thermal conductivity up to 20% by enhancing interfacial thermal conductance and providing transport bridges over grain boundaries of the metal foams, whereas the foam porosity houses the OD for enhanced capacity in the form of latent heat. These composite materials are ideal for ambient energy harvesting in the form of what we call broadband thermal resonators to generate persistent electrical power from ambient thermal fluctuations over large ranges of frequencies. Theory and experiment demonstrate that the harvestable power for these devices is directly proportional to the thermal effusivity of the dominant thermal mass. To illustrate, we experimentally measure persistent energy harvesting from diurnal frequencies at an outdoor location in Cambridge, Massachusetts, extracting as high as 350 mV and 1.3 mW from approximately 10 oC diurnal temperature differences continually over 16 days using high thermal effusivity materials. Thermal resonance devices of this type may provide renewable and persistent energy sources over extended periods.