Ice will slow the blood flow/narrow the blood vessels. Reduce pain, swelling and if any internal bleeding, reduce that a bit also. Ice is usually used for immediate first response to a sudden painful injury.
Heat will extend the blood flow and be used when there is no swelling or inflammation. Like on a nagging injury, including joint pain.
Athletes will use heat treatments (pad's, lotion, creams, etc) before training or general workouts. They want the muscle area warmed up and a healthy blood flow within that area. Guy's will use heat patches/pads. heating lotions/creams,knee/elbow wraps, etc which insure warmth. Even long sleeves workout shirts.
So the general idea will be that heat is used before and during a workout, and ice after a workout. Why so many sports centers have ice tubs/spa's for after a workout. As far as MR P's problem...keep it warm before and during a workout. Ice afterwards, if feeling the need. 15 minutes should be enough time
Known some BB'er who will use a heating element, usually a heat rub or cream, when working arms. And use the same stuff after a workout, to insure that there is a steady supply of blood around the just worked bicep-tricep area, for growth. Most of these guy's also wear full sweats when working out.
Good Luck.