Lets first get this out in the open...A proper Warm-Up is just as important for any BJJ athlete as technical drilling and rolling. Most of the time, I look at some people when they are warming up and they look like they are going through the motions. They are talking about their crappy day at work, how the wife charged way too much on their credit cards, or just about football. These will most likely be the same people that now have to miss training because of injuries.
The primary purpose of a Warm-Up is to elevate the body temperature and prime the neuromuscular and cardiovascular systems for optimal performance, but also get your mind focused on the training session that you are about to be put through.