I wear a compression sleeve for pickleball and racquetball.  It does help keep the arm warm, but I also find that it gives the arm 'cool' feeling due to the compression.  It helps to minimize arm fatigue... that is help reduce the build up of lactic acid and aid with muscle recovery.  And with the slight amount of compression, they aid in better circulation through the arm - thus why there is a sense of a 'cool' feeling in the arm.