Elephants do not seek shelter in caves or other natural formations due to their enormous size, but they do cool off in water and apply coats of mud and dust to their hides to keep themselves cool and protected from the sun. Elephants will even shower to cool down, siphoning water into their trunks and then spurting it out onto their own backs.
Some elephants live in jungle and rain forest environments which afford them shelter. Tree cover keeps the sun off of the elephants' backs, and the moist air keeps their skin from drying out. Most elephants, however, spend most of their time out on the plains.
Mud baths are a communal enterprise for elephants. They help to cover one another in mud, which dries and cracks as they go about their days feeding and traveling until it cracks and crumbles into dust. When this happens, the elephants find a new source of mud and reapply the covering.
Elephants spend most of their time eating or traveling in search of food. They do not have dens or other central locations where they shelter themselves from predators or weather, depending instead on their enormous size and heavy tusks to keep them and their young safe from harm.