--but to my knowledge, the amount of antibody that could be sweated out under steam room conditions is negligible.

Antibodies are specific protein chains--one of the reasons autoantibodies are sometimes referred to as "rogue proteins". They are rather large chain molecules and would not easily pass from serum/plasma through to the cutaneous levels--unless they had already, for some reason, been broken down into component amino acids, in which case they would have already lost their effectiveness as immune agents, anyway.

Think of it this way--if it were possible to sweat out large quantities of antibodies under hot/humid conditions, those people with autoimmune conditions would be flocking to steam rooms and the tropics to reduce their antibody titers, but there's never been any evidence I know of that increased temperatures/humidities reduce autoimmune symptoms. In fact, it IS well known that for many conditions of nerve, heat/humidity actually makes symptoms worse--heat is the enemy of nerve conduction (it tends to increase the electrochemical resistance of the nerve cell membrane and makes it harder for the ionic exchanges to occur). Well-insulated (myelinated) nerves can overcome this, but those with myelin damage . . .cooling vests are very popular among multiple sclerosis patients.

So, if he can otherwise tolerate the steam room, I don't see any reason Alan's visits there would make his IVIg less effective.