Due to the large anomalous Hall effect, magnetic Weyl semimetals can support nonreciprocal surface plasmon polariton modes in the absence of an external magnetic field. This implies that magnetic Weyl semimetals can find novel application in (thermal) photonics. In this work, we consider the near-field radiative heat transfer between two magnetic Weyl semimetal slabs and show that the heat transfer can be controlled with a relative rotation of the parallel slabs. Thanks to the intrinsic nonreciprocity of the surface modes, this so-called twisting method does not require surface structuring like periodic gratings. The twist-induced control of heat transfer is due to the mismatch of the surface modes from the two slabs with a relative rotation.