The paper presents a linear stability analysis of the temperature-dependent boundary-layer flow over a rotating disk. Gas- and liquid-type responses of the viscosity to temperature are considered, and the disk rotates in both a quiescent and an incident axial flow. Temperature-dependent-viscosity flows are typically found to be less stable than the temperature independent cases, with temperature dependences that produce high wall viscosities yielding the least stable flows. Conversely, increasing the incident axial flow strength produces greater flow stability. Transitional Reynolds numbers for these flows are then approximated through an eN-type analysis and are found to vary in approximate concordance with the critical Reynolds number. Examination of the component energy contributions shows that flow stability is affected exclusively through changes to the mean flow. The results are discussed in the context of chemical vapor deposition reactors.