Incorporate furniture in the room with medium shades of wood. Avoid blond woods. Honey, cinnamon and cherry woods are best. They'll complement the orange and red of the room, yet add tones of brown to neutralize it.
Adorn the windows with brown fabric window treatments or wood shutters that match the wood furniture. These touches also work to neutralize the room, keeping it from looking overly red and orange.
Add red, orange and brown throw pillows to the bed to bring all the colors together. Ideally, select a bedspread that incorporates all these colors in a pattern.
Select three to four prominent decorative accessories in a dark blue, azure or navy shade. A vase, trunk, lamp, frame or painting will anchor all the warm colors in the room without being distracting or making the room look busy.