Active control of heat flow at the nanoscale is important for next-generation thermal management and spintronic devices. Here, we report a substantial magnetic modulation of the in-plane lattice thermal conductivity (κL) in monolayer Fe3GaTe2, a two-dimensional van der Waals metal with room-temperature ferromagnetism. Using first-principles transport calculations combined with the special quasirandom structure approach, we demonstrate that the room-temperature κL decreases from 28.94 W m−1 K−1 in the ferromagnetic state to 5.09 W m−1 K−1 in the paramagnetic phase, yielding an intrinsic lattice thermal switching ratio of ∼5.7. Even when accounting for electronic thermal contributions, an estimated total magneto-thermal switching ratio of ∼3.5 is maintained. This massive reduction in κL fundamentally originates from spin-disorder-induced symmetry breaking. In the ferromagnetic state, the out-of-plane flexural acoustic (ZA) mode dominates the lattice heat conduction due to strict selection-rule protection. Upon transition to the paramagnetic phase, localized magnetic disorder destroys the horizontal mirror symmetry (σh), unlocking strong anharmonic scattering channels. This severely suppresses the ZA mode, drastically reducing its relative thermal contribution, and induces a crossover to longitudinal-acoustic-dominated transport. Our findings demonstrate the viability of regulating lattice heat transport via microscopic spin-lattice coupling, providing a quantitative framework for advanced thermal routing and spin-caloritronics.