Thyme also makes a nice groundcover that isn't too invasive. It's pretty, smells nice and does well in hot, dry conditions too. There are lots of different colors as well. Any of the Mediterranean herbs that are low growing would be good plants for your conditions. Rosemary might be a bit tender but if you mulch it deeply with dead leaves or something for the winter, it should survive. The variety "Arp" is more hardy.
But as Rick says, there really is no substitute for mulch. You just need to find the one that works for you. Also if you have neighbors who set out bags of lawn clippings, (and raked leaves in the fall) start collecting them up if you can. Then once frost kills off your garden, pile all that organic stuff on your flower beds as additional mulch and wet it or weigh it down somehow so it stays put for the winter. (lay branches over it, or chicken wire works great) You will gain inches of new good organic stuff by spring! Free, too.
Btw inorganic mulches like rubber and stones really don't help at all. They heat up and the rubber even smells bad when it gets hot. Wood chips break down and add their precious organic fibers to the soil.
