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.