Recall that heat transfer in a certain direction is driven by the temperature
gradient in that direction. There will be no heat transfer in a direction in which
there is no change in temperature. Temperature measurements at several locations
on the inner or outer wall surface will confirm that a wall surface is
nearly isothermal. That is, the temperatures at the top and bottom of a wall
surface as well as at the right or left ends are almost the same. Therefore, there
will be no heat transfer through the wall from the top to the bottom, or from
left to right, but there will be considerable temperature difference between the
inner and the outer surfaces of the wall, and thus significant heat transfer in
the direction from the inner surface to the outer one.