Would You Expect the Neutrino-Antineutrino Background to Be at a Temperature

Would you expect the neutrino-antineutrino background to be at a temperature above or below the 2.75 K of the cosmic microwave background? Why?

A) The neutrino-antineutrino background "escaped" from the primordial fireball long before the CMB. Thus, it has been cooling for a longer time and it should be at a lower temperature.
B) The neutrino-antineutrino background is constantly undergoing annihilation, which produces high-energy gamma rays and heat. Thus, the temperature should be higher than the CMB.
C) The threshold temperature of the neutrino is the highest of any pair of production particles. Thus, the temperature should be higher than the CMB.
D) The neutrino-antineutrino background was produced at an earlier, hotter time in the history of the universe. Thus, this background should be hotter than the CMB.