Yes I too suspect there is no heat transfer from the solid to the air because of a incorrect interface definition. You can verify this several ways. Check the heat transfer flux in the Reports section of the Results Menu. Is there any heat transfer across the fluid-solid interface? Or what is the temperature of the air at the outlet? Your contours above are not really helpful in seeing any change in air temprature. (And is there really some part of your domain that is 1 degree Kelvin?).
Are the solid domains A & B 2D objects (where a thickness is modeled) or does it have a physical thickness with elements through the solid?