I just looked at the map and South India is definitely located in the tropic. Yet most South Indians I saw has long and narrow nose. So I’m not sure about the hypothesis that long and narrow nose heats up air. Or maybe South Indians can handle hot air going up their noses?
Having a tall nose in a tropical area is not going to kill you. Nevertheless, the Indians with the long and tall noses tend to more often be from the north. The Aryans had long, tall noses.
If you look at the true indigenous people of India, the tribals and some of the very primitive hunter gatherer types of the south (Veddoids), many have wide and flat noses, and a number of them have a Negroid appearance such that Afrocentrist morons have tried to claim them as Black.
The Dravidians are probably fairly recent arrivals from 12-17,000 YBP. They probably came first from the Levant, then to Elam and then to India. They may not have had enough time to get tropical adapted, but many Dravidians have developed very dark skin as sun protection.
You can see a wide variety of Indian racial types including Veddoids in this post, The Peopling of India.