I live in the scorching desert of Baja California, Mexico and I have found my groundcovers in what americans refer to as "ice plants" ironically. These are mostly mesemb succulents which include the genera Carpobrotus, Delosperma, Malephora, some Cheiridopsis, some Ruschias among others. Some of these tolerate heat and drought better than others of course, but they're all worth it. Thay have the added of exuberant flower bursts in springtime, and some year round. Another surprising groundcover is Lantana camara. The more water you give it the better it looks but it can make due with as little as one irrigation every 4 or 5 days once established.