Localized cavity resonances due to nanostructures at material surfaces can greatly enhance radiative heat transfer (RHT) between two closely placed bodies owing to stretching of cavity states in momentum space beyond the light line. Based on such understanding, we numerically demonstrate the possibility of ultrabroadband super-Planckian RHT between two plates patterned with trapezoidal-shaped hyperbolic metamaterial (HMM) arrays. The phenomenon is rooted not only in HMM's high effective index for creating subwavelength resonators but also its extremely anisotropic isofrequency contour. The two properties enable one to create photonic bands with a high spectral density to populate a desired thermal radiation window. At submicron gap sizes between such two plates, the artificial continuum states extend outside the light cone, tremendously increasing overall RHT. Our study reveals that structured HMM offers unprecedented potential in achieving a controllable super-Planckian radiative heat transfer for thermal management at nanoscale.