It depends on the type and brand of coconut oil you have.
If it's RBD'ed (Refined, Bleached and Deodorized), it may last for 1-2 years at room temp before it shows signs of rancidity.
Virgin and Extra Virgin coconut oils are the least susceptible to oxidation...and has the longest shelf life of all plant oils (thanks to the natural antioxidants CO contains) . I never refrigerate mine...and is working well.
Try pulling with what you have. If problems arise, continue to use as body lotion.