Well, hot sun and heavy clay soil is not the best environment for grass. You could consider doing something else with the area, plant it in groundcovers, flowers, shrubs and have a standout garden!
But if you insist on having lawn, if you till in compost, aged manure, and gypsum, it will help break up your clay. Fescue might not be your best choice. Bermuda grass, zoysia, or centipede grass might work better.
Here's a little article about types of grass:
Talk to people in your neighborhood that have nice lawns see what they do or talk to the local Master Gardeners or county Extension Service office.