We reanalyse the work of Cleuren et al., Phys. Rev. Lett. 109, 248902 (2012), in the light of Jiang et al. Phys. Rev. B 85, 075412 (2012). The condition for cooling enforces its rate to be exponentially small at low temperatures. Thus, the difficulty with the dynamic version of the third law found by Levy et al., Phys. Rev. Lett. 109, 248901 (2012) and Allahverdyan et al., Phys. Rev. Lett. 109, 248903 (2012) is resolved.
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