If cured and still raw or par cooked in burnt end pieces, then you have time and temp to keep away foodbourne pathogens. If the meat was uncured intact and sugared, salted with a rub with sugar/vinegar bbq sauce I'd find a charcoal grill, gas stove, oven or gas grill to finish and keep cooking. We don't know your variables with other methods of food preservation before refrigeration to give you a little more time to make a wise decision. Most things added to burnt ends: ketchup, mustard, jelly, jams, bbq sauces, vinegars, fermented hot sauce and more are 3.7ph, well below 4.2ph to keep at room temp stable as an alone condiment. This wouldn't keep your burnt ends room temp stable but would keep bacteria on the outside from vegetating quickly and give you time to continue cooking, but we don't know your situation.