Zigzag graphene nanoribbons (GNRs), demonstrating edge magnetism, are fascinating materials for electronic and spintronic applications. In this paper, we investigate with explicit consideration of electron-phonon scattering the Seebeck effect and thermal conductivity at various carrier densities in zigzag GNRs, which undergo antiferromagnetic, ferromagnetic, and paramagnetic transitions. Seebeck coefficients are spin dependent in ferromagnetic zigzag GNRs and can have opposite signs for the majority and the minority spin carriers, which enables the separation of spin carriers spatially under a thermal gradient. The electronic thermal conductivity is small compared to the lattice thermal conductivity, except for GNRs in the ferromagnetic state. A 100% increase in thermal conductivity is expected at antiferromagnetic to ferromagnetic transition. These results demonstrate that zigzag GNRs are also materials of high interest for spin caloritronics.