  We calculate the neutrino mean free path in color superconducting quark
matter, and employ it to study the cooling of matter via neutrino diffusion in
the superconducting phase as compared to a free quark phase. The cooling
process slows when quark matter undergoes a second order phase transition to a
superconducting phase at the critical temperature $T_c$. Cooling subsequently
accelerates as the temperature decreases below $T_c$. This will directly impact
the early evolution of a newly born neutron star should its core contain quark
matter. Consequently, there may be observable changes in the early neutrino
emission which would provide evidence for superconductivity in hot and dense
matter.
