First of all, corn is not a "hot" food. This myth comed from the recommendation to feed corn during very cold weather. The extra energy from the starch in the corn helps the chickens to keep warm. In hot weather the birds are easily able to keep themselves cool by drinking extra water and staying in the shade.
As to the barley, I have also tried to feed it, and it is not very palatable for chickens. It is around 10% protein, and the protein is not very well balanced. If you can get it free, and get the birds to eat it, I guess it's OK for a tiny portion of their diet.
