Cheesecake Cooling Safety

This is my 3rd time baking something and i decided to do something a bit more challenging and made a NY cheesecake. Its currents 1:53 AM and i have to wake up at 6 Am. I baked it, let it cool in the oven with the door closed for 45 minutes and just took it out right now. The question is will the cheesecake be okay sitting on the counter for 4 hours or should i wake up in about 2-2.5 hours and put this puppy in the fridge. Thanks guys😁

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