In this study, based on ab initio calculations and the phonon Boltzmann transport equation, we found that magnetic phase transitions can lead to a significant change in the thermal conductivity of monolayer MnPS3. Around the Néel temperature (78 K) with the antiferromagnetic-paramagnetic (AFM-PM) phase transition, its thermal conductivity increases from 14.89 W mK-1 (AFM phase) to 103.21 W mK-1 (PM phase). Below 78 K, the thermal conductivity of monolayer MnPS3 can be doubled by applying a magnetic field of 4 T, this value has been reported in a previous experiment for the antiferromagnetic-ferromagnetic (AFM-FM) phase transition. Above 78 K, the thermal conductivity of PM phase can be greatly reduced through the PM-AFM magnetic phase transition. In addition to the value of thermal conductivity, the relative contribution ratio between acoustic and optical modes changes with different magnetic phases. The subsequent analyses demonstrate that this regulation originates from the change in lattice parameter, bonding interaction and phonon anharmonicity. In addition, the different effect on the thermal conductivity between the FM and AFM phases was identified by comparing the corresponding phonon scattering characteristics. This study should shed light on the understanding of phonon thermal conductivity in 2D magnets, and provide a practical method for the realization of 2D thermal switching devices, which would enable a broad range of novel applications including energy conversion and thermal management.