My friends in Chennai say it has three seasons: hot, hotter, and hottest. May is squarely in the hottest season. I've been to Mahabalipuram in the heat with a private car and driver. I found that I could take no more than about 20 minutes in the sun and then would have to retreat back to the car to cool down.
Make sure you have a hat, plenty of sun screen and water if you venture out.