Instabilities of thermocapillary flows between counter-rotating disks under microgravity conditions are investigated by linear stability analysis. The basic-state and perturbation equations are solved using the Chebyshev-collocation method. For small Prandtl number liquids (Pr <= 0.01), bifurcation of thermocapillary flows between counter-rotating disks is found to be a 3D oscillatory state for the Coriolis number tau <= 100, except at certain Coriolis number where the most unstable perturbation is 3D stationary state. The critical capillary Reynolds number is a function of Prandtl number, Coriolis number and aspect ratio. Energy analysis shows that the perturbation energy consists of the viscous dissipation, the work done by surface tension and the interaction between the perturbation flow and the basic flow, respectively. For small Prandtl number liquids (Pr <= 0.01), the perturbation energy mainly comes from the interaction between the perturbation and the basic flow, which suggests that the instability mechanism is hydrodynamic. The interaction between the perturbation and the basic flow in the azimuthal direction becomes negative when a moderate rotation is applied on the disks, and the moderate rotation can stabilize the thermocapillary flows for small Prandtl number liquids. (C) 2017 Elsevier Ltd. All rights reserved.