Sure, 40 degrees would work. It depends on what is causing the haze, but it should clear in 2-7 days. If it's a yeast haze, it'll clear fast as the yeast fall out. If it's a chill haze, it might take 7 days or even longer. If it's a fruit beer with a pectin haze, it might never clear!
If the beer is already pretty clear, though, it should be fast.
Broken Leg Brewery
Giving beer a leg to stand on since 2006