Using the transient hot-wire method, thermal conductivity and heat capacity per unit volume are measured for solid and liquid phases and glassy crystal states of cyclooctanol, and information is provided on the phase diagram under high pressure. A new solid phase (III) is detected and characterized as a normal crystal phase, whereas all other solid phases (I, II, IV, V) are characterized as plastic crystal phases. We find evidence that the plastic crystal phases I, II and IV could each be the source for a distinct glassy crystal state. It is argued for phase II that its possession of both a low thermal conductivity and a low dielectric permittivity could be accounted for by assuming restricted reorientational motion of the molecules. The unusual (although small) decrease of thermal conductivity observed through the glassy to plastic crystal transitions may indicate that phonons can couple to reorientational motion in the plastic crystal phases I, II and IV.