Yes, it does support core unlocking. Don't set your eyes too much on that, though. Like I've said many times in the forum, unlocking is a hit or miss. You have around a 60% chance of unlocking the remaining core on the Phenom II X3, so I wouldn't bank on that. Instead, you should look at the performance of each at what you're gonna do. If you're gonna be gaming only and not using too many multi-threaded apps like video encoding or 3D rendering, then for now you're better off with the Phenom II X3. Most games that came out from 2009-10 used three cores but not four. Most games coming out this year are taking advantage of quad-cores, so that may be something to keep looking out for. Having L3 cache vs. having none will give you on average a 10% performance boost in games, but that's also around the same boost you get in multi-threaded games from going to a quad-core from a tri-core. The Phenom II X3 is a C2 revision and the Athlon II X4 is a C3 revision, but both over-clock about the same. As for heat and temps, if you plan on doing heavy over-clocking, the Athlon II will consume more power and generate more heat since it's a quad-core.
TL;DR: get the Phenom II X3. Most games that are out now take advantage of three cores, but not four. L3 cache will bring you an advantage of 10% in games, but the extra core won't help in many.
As for the Phenom II X2, completely dismiss it. Almost all recent games take advantage of three cores and if it doesn't unlock you're in for trouble. You'll have lower performance than both the Athlon II X4 and Phenom II X3 by a noticeable margin.