Exactly. Just so. The 6700 I recommended comes with a cooler. You do not need to buy a separate one unless you want to, which I believe I said before.
The 6700k needs an aftermarket cooler, if you plan to overclock, and does not come with a cooler.
The non-k 6700 is a much higher performer than your 860k, so much so that it's probably at MINIMUM like doubling the performance of your current configuration. Anything you can't game at max settings with the i7-6700 will be due to your graphics card, not the CPU.