It's to capture the body heat, which should increase the healing blood flow into the area. Wearing it too tight can block a normal blood flow into the area. A heat treatment lotion/compound/pack will do the same thing, usually while wearing long sleeve. Even more important while in the gym. It will loosen up tight muscle/joints, etc. Heat works best on chronic injuries
Ice works best on swelling and pain. Ice narrows the blood vessels (heat the opposite). Ice is good on a acute or short term problem. Runners will ice the (usually) knee or ankle joints after working out. With either ice or heat, each should only be applies for short period of 10 to 15 minutes. Let the body part return to a somewhat normal state than repeat the ice or heat treatment.
As rest is a prime healer, I might suggest to Meso_z just that. Perhaps this might only be slight nerve damage, with can be helped with massage, etc. Common logic suggest no curling or pulling motions for awhile. Good Luck.