I Had a Vial of Unopened Unreconstituted BOTOX in the Fridge and the Fridge Broke Overnight. Can It Still Be Used?

a refrig with a closed door that lost power just overnight would not get to 37 Celsius which is almost 100 Fahrenheit...that's much too warm/hot...it like room temperature in the desert and wouldn't be expected for several days/weeks in winter time...and that's if the refrig were outdoors and not in a home kept at 72 - 76 Fahrenheit...and yes the botox wouldn't be much good at that temperature...if on the other hand you mean the temp was 37 Fahrenheit, then the botox is okay if the power was just out overnight...
 

Botox, as well as many other medical products, require pretty strict storage requirements with monitoring, and reconstituted Botox is not indicated to last for very long.  Aside from concerns about non-medical professionals having a home supply of a neurotoxin, the storage in a home refrigerator is questionable.  Frequent opening of the door, as well as the addition and removal of room-temperature items can lead to temperature fluctuations beyond what is indicated (the same reason it is recommended that you do not put eggs on the door of a fridge). 

Additionally, I agree with the comments previously posted.  If you obtained this Botox outside of a medical professional's office (I can't imagine one that would send you home with it), only goodness knows what its' true constitution is.  Many products are sold on the grey market and may be of questionable efficacy and safety, and administration by an untrained individual may lead to unintended adverse effects.