Near-field radiative heat transfer (NFRHT) in many-body systems has opened pathways for enabling novel thermal-radiation applications. In this Letter, we investigate hBN-based enhancement and regulation of NFRHT between two monolayer graphene sheets. On the one hand, we predict that adding an intermediate hBN plate can greatly compensate the exponential damping of evanescent waves due to its hyperbolic modes, thus leading to 1.5 times enhancement of the NFRHT without introducing additional thermal source compared to the graphene-graphene system. On the other hand, we find that adjusting the shift frequency of hBN can greatly change the coupling of its hyperbolic modes and graphene surface plasmon polaritons, thus enabling the remarkable thermal regulation with a ratio of 3.5. We hope that our work may facilitate nanoscale thermal management in many-body systems and benefit the comprehension of hBN-based photon tunneling.