Thermal transport is a pivotal probe for studying low-energy, charge-neutral quasi-particles in insulating magnets. In this Letter, we report an observation of large magneto-thermal conductivity and thermal Hall effect (THE) in a van der Waals antiferromagnet FeCl2. The magneto-thermal conductivity reaches over ~700%, indicating strong magnon-phonon coupling. Furthermore, we find an appreciable thermal Hall signal which changes sign concurrently with the spin-flip transition from the antiferromagnetic state to the polarized ferromagnetic state. Our theoretical calculations suggest that, in addition to the Berry curvature induced at the anticrossing points of the hybridized magnon and acoustic phonon modes of FeCl2, other mechanisms are needed to account for the magnitude of the observed THE. The data of figures presented in this paper is available at this link.