Pop the cheesecake in the refrigerator, covered, to cool for about 4 hours. When you're ready to make the toppings, get all the caramel sauce ingredients prepared. This means having the butter and cream measured and ready to grab and go, because you won't have time to look for it when you need it.
Get out a heavy-bottomed metal (not nonstick; see the notes for tips on caramel) saucepan and set the water and sugar on a medium-high heat. Literally don't stir the sugar at all, just let it melt and dissolve by itself. You can swill the saucepan around a bit to distribute the sugar and make sure none is burning, but DO NOT STIR. Trust me.
When the sugar is melted and is a nice, rich amber color (this takes about 15-20 minutes of careful pan watching), quickly add the butter, stirring constantly to melt. Be absolutely careful as things will splash and froth and molten sugar is a billion times hotter than boiling water. Once the butter is melted, take it off the heat and wait five seconds before dumping the cream in (again, BE CAREFUL). Stir well until the sauce is thick and well combined, then set aside to cool.