The interaction between the drift-current biased graphene plasmonics and the hyperbolic phonon polaritons of α-MoO3 provides a promising way to manipulate near-field radiation heat transfer (NFRHT). Through examination of the drift biased graphene/α-MoO3 heterostructure, it has been discovered that drift-current applied to the graphene effectively enhances photon tunneling. Consequently, they dynamically modulate the coupling effect of the two excitations, thereby offering a reliable pathway for the modulation of NFRHT. Furthermore, the influencing mechanism of vacuum gaps on nonreciprocal NFRHT with different drift-current rates is revealed, and it is discovered that the vacuum gaps can filter the nonreciprocal surface plasmon polaritons with high nonreciprocity. Our findings make it possible to manipulate nanoscale thermal rectification and noncontact thermal modulation.