Solid-state cooling employing barocaloric materials, especially plastic crystals, paves a promising way for eco-friendly refrigeration. However, inadequate understanding of the thermal properties hinders their practical applications. Here, we take α-pentaerythritol crystals as an example and reveal that the thermal transport is anisotropic, and the lattice dynamics is highly anharmonic. More importantly, we find that the two lowest-energy resonant phonon modes, associated with two mutually perpendicular molecular rotations, play critical roles in thermal conductivity and phase stability. The two optical modes suppress the acoustic branches by the avoided-crossing effect and hybridize with and strongly scatter acoustic phonons, further hindering thermal transport in α-pentaerythritol crystals. Furthermore, pressure can largely tune the rotational dynamics, reduce the resonance, and increase the phonon transmission and by adjusting the pressure from 0 MPa to 3500 MPa, an increase of 108% and 103% in in-plane and out-of-plane thermal conductivity, respectively, can be achieved. Our work provides a microscopic understanding of the rotational dynamics in α-pentaerythritol crystals, which can facilitate designing molecules to achieve a better barocaloric effect with more excellent thermal properties.