I briefly review the formation of color superconductivity which happens in compact stars. Below the temperature scale set by the gap in the quark spectrum, transport properties are determined by collective modes. We compute the thermal conductivity, kappa, of color-flavor locked (CFL) quark matter in the frame of kinetics theory. We present and compare the result with previous estimates. We also conclude a CFL quark matter core of the compact star becomes isothermal on a timescale of a few seconds. Moreover, we compute the thermal conductivity and sound attenuation length of a dilute Fermi gas, which help us comment on the possibility of extracting the shear viscosity of the dilute Fermi gas at unitarity using measurements of the sound absorption length.
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