Understanding lattice thermal transport in magnetic materials is crucial for their application in spintronic devices. However, the effects of dimensionality and magnetic order and disorder on phonon heat transport remain under debate. Here, we systematically investigate the lattice thermal conductivity ${\kappa }_{\ell }$ of monolayer, bilayer, and bulk ${\mathrm{CrI}}_3$ in both ferromagnetic (FM) and paramagnetic (PM) phases by developing an integrated computational framework that combines a type-differentiated moment tensor potential with the phonon Boltzmann transport equation. In this framework, spin-up and spin-down Cr atoms are explicitly distinguished, enabling the PM phase to be accurately described as a disordered local-moment state rather than as a nonmagnetic approximation. The results demonstrate that ${\kappa }_{\ell }$ in ${\mathrm{CrI}}_3$ exhibits a strong dimensional dependence. At 300 K, ${\kappa }_{\ell }$ decreases monotonically from monolayer to bulk in both FM and PM phases, with the reduction reaching as high as 53% and 55%, respectively. Such pronounced suppression is mainly caused by the weakening of low-frequency heat-carrying phonons, shortened phonon lifetimes, and reduced mean free paths. In contrast, the impact of magnetic disorder on thermal transport is found to be relatively weak, leading to only a 9%–14% reduction in ${\kappa }_{\ell }$. This weak dependence is consistent with the small differences in both harmonic and anharmonic interatomic force constants between the FM and PM phases, as well as the weak magnetic exchange interactions in ${\mathrm{CrI}}_3$. Our results provide a clear microscopic understanding of coupled spin-lattice thermal transport and establish an efficient computational framework. This framework enables reliable prediction of thermal transport properties in complex magnetic phases and holds promise for promoting the development of energy-efficient magnetic devices for information processing and storage.

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• Lattice thermal conductivity
• Magnetic order
• Thermal transport
• Layered crystals
• Density functional calculations
• Lattice-Boltzmann methods
• Machine learning