I heated (in a 900W microwave) some pre-cooked, shop-bought barbecue sauce-covered chicken wings. Unfortunately, instead of doing so for the required two minutes and thirty seconds, I only heated them for 1 min 40 secs. When we started to eat them a few minutes later, they were noticeably lukewarm. We didn't eat much at all, but I am worried about food poisoning. Are we likely to fall ill? 
It's perfectly safe. If it's pre-cooked then it is safe to eat cold, hot or lukewarm. It's true that room temperature is the happy range for the microbes that cause foodborne illness to grow, but that takes at least a couple of hours to develop. Just nuke it again until it's hot. 