1/2" ID, 5/8" OD is 1/16" walled tubing. You'll get more kinks than you'd get with 1/8" walled tubing (Tygon or other), but it should fit on the barbs fine without heating (boiling). If, however, you find that it's kinking when you're making bends with it, then by all means, boil it and then use extra clamps to keep it round when you make the bend. Tygon molds very well so if you get it into the correct shape after boiling it, it'll stay in that shape after it cools down--the water in the cooling system isn't hot enough to cause it to loose the shape you put it in.
Edit: I didn't answer your original question. Boiling the tubing allows it to stretch more (or more easily) than it would otherwise. So, if you're putting 7/16" ID tubing on a 1/2" (8/16") barb having the tubing stretch easier is beneficial. When you're using 1/2" ID tubing on a 1/2" barb it isn't necessary.