Your recipe probably didn't call for using different temperatures. A little trick in baking your cheesecake and avoiding cracks is to use an initial high heat to warm things up and then turn down after 15 minutes. If I remember correctly bake at 350F for 15 min, then 275F. A cheesecake is (usually) a custard which uses eggs but you have to take care that they don't work as a leavener. The reason for turning down the heat is to limit the expansion and to cook the center without over cooking the top. If the top cooks first and then the center expands while cooking you'll get cracks. And yes always use a water bath and non-stick spray or butter on the sides.I've had great result in turning down three times with a finished temp of 240F. But, If interested check out some recipe's using gelatin and doesn't call for baking at all.

A couple of possibilities: It could have been overdone - you want the center 3 or so inches to be wobbly when you pull it out of the oven, it will continue to cook for a bit. Also make sure to use a water bath, which keeps the temperature throughout the cheesecake more consistent. A second possibility is that the sides stuck to the rim of the springform so while it cooled and shrank, it had to split in the middle. To prevent this you need to run a paring knife around the edges as soon as it come out of the oven.