The thermal conductivity κ of cyclopentane clathrate hydrate (CP CH) of type II was measured at temperatures down to 100 K and at pressures up to 1.3 GPa. The results show that CP CH displays amorphous-like κ characteristic of many crystalline clathrate hydrates, e.g., tetrahydrofuran (THF) CH. The magnitude of κ is 0.47 W m⁻¹ K⁻¹ near the melting point of 280 K at atmospheric pressure, and it is almost independent of pressure and temperature T: ln κ = −0.621−40.1/T at atmospheric pressure (in SI-units). This is slightly less than κ of type II CHs of water-miscible solvents such as THF. Intriguingly, unlike other water-rich type II clathrate hydrates of water-miscible molecules M (M·17 H₂O), CP CH does not amorphize at pressures up to 1.3 GPa at 130 K and also remains stable up to 0.5 GPa at 240 K. This shows that CP CH is mechanically more stable than the previously studied water-rich type II CHs, and suggests that repulsive forces between CP and the H₂O cages increase the mechanical stability of crystalline CP CH. Moreover, we show that κ of an ice-CH mixture, which often arises for CHs that form naturally, is described by the average of the parallel and series heat conduction models to within 5% for ice contents up to 22 wt%. The findings provide a better understanding of the thermal and stability properties of clathrate hydrates for their applications such as gas storage compounds.