Why biofeedback would help this problem: The symptoms of Raynaud's syndrome (blanching and pain eventually followed by cyanosis) are caused by spasms in the vascular system in at least the fingers and toes with possible involvement of the ears and nose. The reason some people experience these spasm while others don't is really not understood. The spasms are usually set off by sudden cooling of the extremities and / or psychological stress responses. The inability to maintain the fingers at a minimal temperature leads to onset of the spasms which then cause the pain and other symptoms associated with Raynaud's disease.
Anyone will go into vasospasm if the hands are cold enough and then are suddenly cooled even more because the individual's own "catastrophic break point" is reached below which spasms occur. The difference between normal people and those having Raynaud's phenomenon are that Raynaud's sufferers (1) have cooler hands and feet than most people all of the time and (2) they are more reactive to cooling stressors such as sudden exposure to a cool breeze or a freezer than are most people. This combination means that they are always closer to their "break point" than the rest of us and that they will have severe spasms with much cooling less stress than we would.
Vasoconstriction due to psychological stress would be just as effective a way to initiate a spasm as any physical stress. Thus, temperature biofeedback is used to train patients to keep their hand temperatures elevated to as close to normal as possible all the time and to keep them warm even when cooling stresses take pace.