Today marks the beginning of Agni Nakshatram 2016, the hottest days according to the Tamil calendar. Incidentally it also coincides with the peak summer period for most of Tamil Nadu. June / July could see more uncomfortable days for Chennai thanks to the very strong Westerly Land breeze that prevents moderating sea breeze to move in. It is during this period of May typically Chennai its highest absolute temperature peaks for the year.
But Agni Nakshatram 2016 possibly could get off to a sedate start particularly for coastal areas under the influence of strong Southerly winds during the early part of the day and more Easterly winds subsequently. 
Under the influence of Line of Wind Discontinuity that is running all along the Peninsular India from Marathwada to Comorin Sea large parts of South India is likely to get evening thunderstorms with places in Telengana likely to see isolated hailstorms as well. Some parts of Western Tamil Nadu around Dharmapuri / Erode / Salem could possibly get some isolated rains as well.
Temperatures across South India is likely to be marginally lower compared to the last few days bringing a sedate start to Agni Nakshatram 2016. The interiors of Tamil Nadu are likely to see temperatures in the region of around 39 /40 degrees while coastal Tamil Nadu is likely to be under moderately hot conditions as well. Thanks to wind discontinuity Telengana is likely to enjoy some much needed respite from the heat wave like conditions.
#Chennai could see a moderately hot day with day time maximum temperature touching around 36 degrees with the suburbs possibly hotter by a degree or so compared to the city. Mornings could be cloudy thanks to the Easterlies continuing still.