Referring to the quotes from the below links;
• “Baked cheesecake should be refrigerated as soon as it is cool or it
may develop harmful bacteria from heat resistant spores.”
http://www.canfightbac.org/cpcfse/en/cookwell/ask/dairy/#2085
• “Foods made with eggs and milk such as pumpkin pie, custard pie and
cheesecake, must first be safely baked to a safe minimum internal
temperature of 160 °F. Then, they must be refrigerated after baking.
Eggs and milk have high protein and moisture content and when these
baked products are left at room temperature, conditions are ripe for
bacteria to multiply. It's not necessary to refrigerate most other
cakes, cookies or breads unless they have a perishable filling or
frosting.”
http://www.fsis.usda.gov/factsheets/Hotline_Answers_Panic_Button_Questions/index.asp
When to throw it out; a quote from the link below;
“Refrigerator Foods When to Save and When to Throw It Out
FOOD..................... Held above 40 °F for over 2 hours
Cheesecake............ Discard
http://www.fsis.usda.gov/factsheets/keeping_food_safe_during_an_emergency/index.asp