How long can I leave a freshly baked cheesecake out before it goes in the refrigerator?
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