My mom left bacon grease sitting in a container on the back of the stove till the day she died 4 years ago. She did not have air conditioning either. However, she used it for seasoning all the time. Also, back in the days before refridg. meat processed some kind of way and packed in rendered fat.

To answer your question, if it is used within the day, I would leave it out, otherwise keep it in the fridg., if it is not used within a week, I find it gets old tasting regardless of where it is kept.

I hope this helps.