Plated mail, India, 16th-17th century AD

The main problem might not be the chain mail. Right, it heats up and at some point it might hurt to touch it. I don't know about India, but in Europe chainmail has often been worn with padded armour to compensate for the weaknesses of the mail and that has almost not breathability. You can get a bit of cooling when it is drenched with sweat or you can make it wet, but still not the best gear for hot weather. You will need to drink a lot of water. My record was close to 6 litres of water wearing mail and padded armour in the summer along with physical activity.