Is it considered abandonment, and is the husband sinful if he sleeps in an adjacent room to the bedroom due to humidity in the latter, even though he asks his wife to join him and she refuses and accuses him of abandonment?

The husband does not sin, nor is he considered to have abandoned his wife, if he sleeps in another room for rest. Rather, the wife must fulfill his desire and come to him in that room. If she refuses, that is an act of defiance (nushooz) and abandonment of her husband's bed, and she deserves Allah's wrath and the curse of the angels if her husband spends the night angry with her. The wife must obey her husband in matters that do not involve disobedience to Allah.