Threshold photodetachment spectroscopy has been performed on the molecular anion CN- at both 16(1) K and 295(2) K in a 22-pole ion trap and at 295(2) K from a pulsed ion beam. The spectra show a typical energy dependence of the detachment cross section yielding a determination of the electron affinity of CN to greater precision than has previously been known at 31 163(16) cm-1 [3.864(2) eV]. Allowed s-wave detachment is observed for CN-, but the dependence of the photodetachment cross section near the threshold is perturbed by the long-range interaction between the permanent dipole moment of CN and the outgoing electron. Furthermore, we observe a temperature dependence of the cross section near the threshold, which we attribute to a reduction of the effective permanent dipole due to higher rotational excitation at higher temperatures.