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If you want my personal thought, which may not be correct, I think maybe in the next day it will ROT and stink. If it's a type of cheese, yeah, it will stink and rot. Another answer Cream cheese should not sit out at room temperature for more than 2 hours. Less time is better.
I think you're safe. Cheesecake is better at room temperature but best stored cold. Figure it didn't cool completely until about 12 am. At that point it sat for about 6 hours. You can leave cream cheese out for about 6 hours but not much more than that. Give it the ole sniff and taste test. If it's a little sour than don't risk it.