The thermal properties of graphane, hydrogenated graphene, are surprisingly underreported, and there are commonly held opposing views on its thermal conductivity. While hydrogenation negatively affects the thermal conductivity, the exact nanoscale thermal transport properties of graphane are still poorly understood and the mechanisms involved remain obscure. The thermal transport properties of graphane nanoribbons were investigated theoretically by performing molecular dynamics simulations. The effect of hydrogenation degree was evaluated, and comparisons of thermal conductivity were carried out between graphene and graphane or between different forms of spatial isomerism. The order-of-magnitude difference in thermal conductivity between graphene and graphane ribbons was determined accordingly. The rule of mixtures was applied to provide the theoretical upper and lower bounds on the thermal conductivity. A theoretical analysis was made to assess the correlation between the thermal conductivity and the peak amplitude of out-of-plane vibration. The results indicated that graphane shows great promise for flexible tuning of thermal properties. The extent of hydrogenation admits a convenient chemical dial for tuning the thermal conductivity. The thermal conductivity of graphane isomers decreases successively in the order of the chair, boat, and stirrup configurations. The thermal conductivity of graphene and graphane differs by one order of magnitude or more, depending upon spatial isomerism and out-of-plane vibration amplitudes. For the stirrup configuration, the thermal conductivity is decreased by a factor of at least 20, and by about a factor of 10 when semi-hydrogenation occurs. The thermal conductivity of partially hydrogenated graphene can be predicted by applying the rule of mixtures. The results have significant implications for understanding of the relations between spatial isomerism and thermal properties.