I am in no position to answer your question scientifically but out of some experience in sports I can tell you that warming up is extremely vital to your stretching. You don't need to warm up for long but little is advisable. For example you could start by mobility exercise; like rotating your arms and torso. If you like you could just jog around or if you prefer you could do it on spot. Warm muscles are much more easily stretched than cold ones, always warm up first to get blood circulating throughout the body and into the muscles. A warm-up should be slow and pleasant. If you don't you might risk tearing or injuring the muscle.