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The thermal conductivity, κ, of solid triphenyl phosphite was measured by using the transient hot-wire method, and its temperature and pressure dependencies were analyzed to understand heat transfer processes in the solid polymorphic phases, as well as in the glass and the exotic glacial state. Phase transformations and the structural order of the phases are discussed, and a transitional pressure–temperature diagram of triphenyl phosphite is presented. The thermal conductivity of both the crystalline and disordered states is described within the theory of two-channel heat transfer by phonons and diffusons in dielectric solids. In the glass and glacial states, the weakly temperature-dependent (glass-like) κ is described well by the term associated with heat conduction of diffusons only, and it can be represented by an Arrhenius-type function. In the crystal phases, the strongly temperature-dependent (crystal-like) κ associated with heat transfer by phonons is weakened by significant heat transfer by diffusons, and the extent of the two contributions is reflected in the temperature dependence of κ. We find that the contribution of diffusons in the crystal phases depends on pressure in the same way as that in amorphous states, thus indicating that the same mechanism is responsible for this channel of heat transfer in crystals and amorphous states.