Hello
In hot climates, elephants tend to spray water on themselves. The water evaporates off of their skin by taking up heat emitted in the form of radiation by the elephant. If they did not splash water, they won't be able to sustain their normal homeostatic temperatures and so would overheat. This is because of their large size thus their large surface-area. Also, by virtue of their size, they contain a great deal of muscle and fat around their organs. This helps them in winter, but say in summer, to avoid overheating, they usually spend most of their times next to lakes or rivers to cool down. Kind of like humans when it's hot, we tend to go to the beach or swimming pool. When we're cold, we lay down in a fetal position which reduces the surface area by which we are losing heat to stay somewhat warm.
As for the elephant ears, blood vessels contain baroceptors and osmoceptors that maintain pressure and fluid flow during homeostasis. They act as sensors. When temperatures rise, these blood vessels tend to dilate in order to bring in more water and oxygenate blood over the surface allowing the regulation of temperature. We tend to see elephants flapping their ears around a lot. This is sort of similar to monitoring the temperature and vasodilating but also to create air circulations around just like a fan.
I hope this helps
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