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This study examines the effects of shear induced wrinkles on the thermal transport properties of hexagonal boron nitride (hBN) ribbons. Reverse nonequilibrium molecular dynamics simulations were performed using a Tersoff force field to estimate the thermal conductivity of both undeformed and shear-wrinkled hBN nanoribbons of various widths and lengths. The results indicate that the impact of shear induced wrinkling on thermal conductivity is more evident in narrower ribbons, where lattice distortion and bond stretching are more severe. In contrast, wider ribbons exhibit relatively milder distortions and thus less reduction in heat dissipation capability. Notably, the bulk thermal conductivity of the narrowest hBN ribbon simulated in the present study decreased by 47 % at a shear strain of 0.3 compared to its undeformed structure, whereas the widest ribbon simulated in the present research study showed only a 25 % reduction. Phonon density of states analyses revealed substantial alterations in low-frequency acoustic phonons under shear-wrinkling, with flexural acoustic modes identified as the primary contributors to thermal performance degradation. The findings of this study are expected to inform the design of new materials with improved heat dissipation capabilities for flexible electronics.