We analyze the heat current traversing a quantum dot sandwiched between a ferromagnetic and a superconducting electrode. The heat flow generated in response to a voltage bias presents rectification as a function of the gate potential applied to the quantum dot. Remarkably, in the thermally driven case the heat shows a strong diode effect with large asymmetry ratios that can be externally tuned with magnetic fields or spin-polarized tunneling. Our results thus demonstrate the importance of hybrid systems as promising candidates for thermal applications.