Dispersive metamaterials are artificial composite media with magnetodielectric losses so that they naturally radiate in their surrounding. Here we theoretically investigate both radiative and nonradiative heat exchanges between two metamataterials. We show that the presence of magnetic surface modes and the ferromagnetic behavior of materials close to their magnetic resonance yield novel channels for energy transfer. These results pave the way to the design of innovative structures to manage the noncontact heat exchanges.