You don't need a seperate cooler for a lauter tun and a sparge arm if you're going to fly sparge, it's just a little easier. I don't have either. I just heat up the sparge water in another pot and then carefully pour it one quart at a time on top of the mash with a 1 qt. pyrex measuring cup. I have a 5 gallon cooler for a mash tun, so the grain bed is nice and thick. No problems with channeling or stuck sparges.