The thermal conductivity κ(T ) of the fully ordered stable phase II, the metastable phase III, the orientationally disordered (plastic) phase I, as well as the nonergodic orientational glass (OG) phase, of the glass former cyclohexanol (C6H11OH) has been measured under equilibrium vapor pressure within the 2–200 K temperature range. The main emphasis is here focused on the influence of the conformational disorder upon the thermal properties of this material. Comparison of results with those regarding cyanoclyclohexane (C6H11CN), a chemically related compound, serves to quantify the role played by the terminal groups -OH and -CN on the phonon scattering processes. The picture that emerges shows that motions of such groups do play a minor role as scattering centers, both within the low-temperature orientationally ordered phases as well as in the OG states. The results are analyzed within the Debye-Peierls relaxation time model for isotropic solids comprising mechanisms for long-wave phonon scattering within the OG and orientational ordered low-temperature phases, as well as others arising from localized short-wavelength vibrational modes as pictured by the Cahill-Pohl model. By means of complementary neutron and Raman scattering we show that in the OG state the energy landscapes for both compounds are very similar.