  We study theoretically the anisotropic magneto-Peltier effect, which was
recently demonstrated experimentally. A first-principles-based Boltzmann
transport approach including the spin-orbit interaction shows that Ni has a
larger anisotropy of the Peltier coefficient ($\Delta \Pi$) than Fe, consistent
with experiments. It is clarified that spin-flip electron transitions due to
the spin-orbit interaction are the key in the mechanism of the large
anisotropic magneto-Peltier effect. Using our method, we further predict
several ferromagnetic metals with much larger $\Delta \Pi$ than that of Ni.
