By performing warm-up routines, you actually do literally just that - warm up the body. Internal body temperature can't raise by a large amount, or you would have all the symptoms of a fever. Nevertheless, the temperature in the muscles can, and should, be raised slightly in order to dilate blood vessels and loosen muscles.
That dilation leads to greater blood flow, which helps oxygenate muscles and remove the waste products of cellular activity. Warm muscles are looser, more supple and flexible. That reduces stiffness and lowers resistance to larger movements. That helps reduce the risk of injury and prepares the body for high-performance activity.
A good warm-up also raises the heart rate, respiratory capacity and the overall metabolic level. Among other benefits, this helps deliver nutrients to muscles that will be useful for the workout to come. Warm-ups help lubricate joints, too, as well as lowering the risk to stretched tendons and tears.
No matter what kind of sport or workout you favor, having a well-functioning cardiovascular system and supple joints and muscles are essential for peak performance and low risk of injury.
A 10-15 minute warm-up period, including static and dynamic stretching activities, should be a low-intensity version of the routines that will be undertaken when the warm-up is complete.
Focus the non-stretching aspect of your warm-up more on the specific types of movement called for by the sport or activity you plan to engage in. If you plan to jog five miles, take a brisk walk, followed by a few gentle laps of a hundred yards or less. If you plan to play tennis or golf, spend a few minutes on low-speed, low-impact swings.
As you progress through the warm-up, gradually increase the speed and range of movement. This helps prepare the body and mind both.
Making the increase gradual helps increase the cardio and lung systems, and slowly cranks up needed body chemicals systems without depleting them. It helps gear up the mind for a high performance routine or sports event, in a way that static or even dynamic stretches won't.
Like any physical activity, don't overdo it. Don't warm-up too much or too fast. The idea is to prepare the body for a workout, not perform one.
At the end, you'll be ready to perform the sport or workout of your choice at peak level with minimal risk of injury.