In most cases, we talk about thermal mass as something that absorbs and stores useful heat from the sun's light, releasing it when your home gets colder to maintain a comfortable indoor temperature. However, it is possible to use thermal mass as an effective cooling mechanism.
Hot days, cold nights
In regions where the days are very hot and the nights are relatively chilly, thermal mass can make a significant dent in a home's cooling load. The mass works as it does in every case: it absorbs light and heat during the daytime, releasing that heat when the home cools. Since the night is much cooler than the day, the extra heat accumulated by the thermal mass can be vented by simply opening a window or two and allowing it to escape.
The great thing about this is that it works without any kind of adjustment to the home – the mass absorbs and releases heat exactly as it does in winter, but the extra ventilation purges the stored heat. It even works with sunspaces and thermal storage walls. This approach works best in hot, arid climates such as in the desert, where the nights are so much cooler than the days.
Another tactic that works well in such climates is exterior thermal walls. They need to be built very thick – two feet of adobe wall is quite normal. The way they work is the same as in milder climates: the sun's light warms the wall and the heat is stored. It slowly works its way inwards through the wall to the cooler interior. But if the wall is thick enough, the day ends before the heat gets indoors. The outside temperature drops below the indoor temperature and the heat stored in the thermal walls reverses direction, heading out towards the exterior. The heat goes back and forth, day and night, without ever arriving inside the home.
Hot days, hot nights
In regions with hot, humid climates, exterior thermal walls may not work. The nighttime temperatures may not be low enough to draw the heat out, so the home will slowly heat up. If this happens, the home will eventually have so much heat stored in the walls that it will be very difficult to sufficiently purge the warm air from inside.
However, interior thermal mass can still be useful. Opening the windows at night won't get rid of the accumulated heat, but you can run an active cooling system for a reduced period of time to vent as much as possible. The cost of running the air conditioning for a couple of hours in the evening is lower than running it during the day, when the cooling load is higher.