Practically all USB enclosures are, well, enclosed. The shell is typically open on one side and you slide the inside completely out. You can't do something like expose one side unless you're handy with a dremel tool.
Regarding heat, 2.5" drives don't generate enough heat for it to be a problem. 3.5" drives do get toasty if they're doing something extended, but you can get enclosures that have active cooling in them. Otherwise a lot of them are made of metal and there's plenty of contact between the drive and the enclosure that the enclosure acts as a heat spreader.
You could also get a USB hard drive dock if you're not going to use the drives all that often.