Owing to the coupled ferroic order parameters, two-dimensional ferroelastic-ferroelectric multiferroics have emerged as promising candidates for nonvolatile memories, multifield-responsive sensors, and intelligent thermal management devices. However, realizing such functionalities in intrinsically nonferroic systems like monolayer hexagonal boron nitride ($h$-BN) remains a critical challenge. Here, we demonstrate that hydrogenation could induces robust multiferroicity and switchable thermal transport in monolayer $h$-BN. First-principles calculations reveal that hydrogenation triggers an $s{p}^2$-to-$s{p}^3$ rehybridization, breaking the pristine $C_3$ rotational symmetry, generating spontaneous polarizations of 160.79 and 90.53 $\mu \mathrm{C}/{\mathrm{cm}}^2$ in $\alpha \text{−}{\mathrm{H}}_2\mathrm{BN}$ and $\delta \text{−}{\mathrm{H}}_2\mathrm{BN}$, far exceeding conventional ${\mathrm{BaTiO}}_3$ ($\sim 26$ $\mu \mathrm{C}/{\mathrm{cm}}^2$ ). Meanwhile, the ferroelastic-ferroelectric switching barriers are 0.15 and 0.12 eV/atom, guaranteeing ultralow-energy bit operations. By combining machine learning interatomic potentials with the phonon Boltzmann transport equation, we further show that $\alpha \text{−}{\mathrm{H}}_2\mathrm{BN}$ and $\delta \text{−}{\mathrm{H}}_2\mathrm{BN}$ exhibit anisotropic lattice thermal conductivities (considering both three-phonon and four-phonon scattering) of 133 (327) and $140\left(84\right)\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$ along the $xx$ ($yy$) direction. The thermal conductivity can be reversibly switched via ferroelastic-ferroelectric coupling, achieving ON/OFF ratios of 2.46 and 1.67. These results clarify the combination of giant ferroelectricity, low switching energy, and real-time tunable thermal conductivity endows $\alpha \text{−}{\mathrm{H}}_2\mathrm{BN}$ and $\delta \text{−}{\mathrm{H}}_2\mathrm{BN}$ as compelling candidates for monolithic devices that unify nonvolatile data storage and adaptive thermal management.

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• Ferroelasticity
• Ferroelectricity
• Phonons
• Thermal conductivity
• Thermal properties
• First-principles calculations