have you seen his shoulder, can you say that it is indeed swollen? there is no indeed definite way to say there is even inflammation, i was seeing if cold or warmth helped more because the main cause of a frozen scapula and rotators cup is due to neural impedement, if there is neural impedement(which it does sound like due to the radiation of the pain) then warmth would help it more seeing as a pinched nerve responds severly negative to cold stimuli... you dont want to tell people who have a frozen shoulder to try to keep it in place...think about it...its frozen...its already in place, he should try to keep it moving as much as possible.
have you got your shoulder manipulated yet. My dad had frozen shoulder and had to get put under then they manipulated his arm all the way back and he could actually move his arm after.
try using a cold compress for 20 minutes then a warm compress for 20 minutes this might help...if not go to your doctor he could possibly give you a cortico-steroid injection at the site...and that would kill any inflammation and most of the pain...best of luck keep me posted