Do I need to store hard lemonade cold?

[flander]

I made a hard lemonade similar to this:
https://www.homebrewtalk.com/f25/hard-lemonade-my-crazy-way-150111/

Just wondering if something like this needs to be stored cold, ie in my fridge? or will it stay good at room temp? or cellar temp? Should I be worried to leave it out?

 

[CandleWineProject]

They added sorbate and sulfate, so it would have effectively killed of the yeast if the cold didn't (which it doesn't always). Therefore, if you follow that, it shouldn't matter what temp you store it at.