I wonder how well would aluminium barrel shrouds would work as a cooling solution. The only example I know (other than the Lewis gun with its forced air cooling) is the Chauchat, where it did not work, because as the aluminium expanded against the receiver it froze the barrel in place, and that is not a brilliant thing in a recoil operated weapon. But in theory you could make a straight and featureless barrel and then put an extruded aluminium shroud with lots of cooling fins on it, and in theory it should not affect the ballistics of the barrel (other than adding extra weight), unlike cooling fins that are machined directly into the barrel.