Air traffic effects high cloudiness and therefore the Earth's radiation budget by producing contrail cirrus. Contrail cirrus comprise of line-shaped contrails and irregularly shaped ice clouds that originate from them. The warming effect of contrail cirrus is disproportionally large at night, since at daytime the cooling due to the short wave cloud albedo effect acts toward compensating the long wave warming effect. Therefore it has been suggested to restrict air traffic to daytime in order to reduce its climate impact. The potential for reducing the contrail cirrus radiative forcing by shifting air traffic to daytime depends on the diurnal cycle of contrail cirrus coverage which is in turn determined by the diurnal cycle of air traffic and the contrail cirrus lifetimes. Simulations with a global atmospheric general circulation model indicate that the annual mean contrail cirrus coverage may be almost constant over the day even in areas where air traffic is close to zero at night. A conceptual model describing the temporal evolution of contrail cirrus coverage reveals that this is due to the large variability in contrail cirrus lifetimes in combination with the spreading of contrail cirrus. This large variability of lifetimes is consistent with observational evidence but more observations are needed to constrain the contrail lifetime distribution. An idealized mitigation experiment, shifting nighttime flights to daytime, indicates that contrail cirrus radiative forcing is not significantly changed.