We numerically study the tuning of the radiative heat transfer between a spherical InSb nanoparticle in the vicinity of a flat SiC surface assisted by a static magnetic field. By changing the value of the applied magnetic field, the dielectric function of the nanosphere becomes anisotropic due to the excitation of magneto-plasmons. In the dipolar approximation, the plasmon resonance of the particle splits into two additional satellite resonances that shift to higher and lower frequencies as the field increases. When one of the particle resonances overlaps with the phonon-polariton frequency of the SiC surface, an enhancement of the heat transfer of two orders of magnitude is obtained. To understand the tuning of the radiative heat transfer, we present a detailed analysis of the nature of the modes that can be excited (surface, bulk, and hyperbolic).