One of the often ignored problems of near light speed travel is that as the redshift of the cosmic microwave background radiation in the direction you're traveling decreases, it becomes rapidly warmer and warmer. The effect of the dipole would also exacerbated by the realities of relativistic beaming, as the far surface background of space grew warmer, the warm area would spread out to cover almost the whole sky as you approached the magic number. By about 299760km/s you'd be cooked by the sky's microwave intensity.