Speed: Compared to my 2012 MBP, it's super fast. So far, it seems to easily keep up with my customac on common tasks (see my signature). I have yet to test it with things like games, but I don't expect it to excel at that. Just from watching the Unengine benchmark, it doesn't really compare much to a desktop GPU - even my old GTX 760. I'm sure it will be fine for other intensive tasks though, like photo and video editing.
Noise: Very quiet, usually silent
Battery: Haven't used it long enough to know this yet.
Heat: It was pretty warm at first, but that was probably due to setting up all my apps and syncing cloud data, etc. During that time, the Touch Bar area was very warm to the touch, and the exhaust area behind the MacBook got uncomfortably warm while in my lap. It has since cooled down a ton, and isn't warm at all now.