That can get long and tiring if you aren't flying!
There are direct flights and trains for this journey. Catching a direct flight is the fastest way to do this journey. Direct trains are available as well. New Delhi (Delhi) to Chennai (Tamil Nadu) distance is 2179 km and you can get there by flight in just over 2 hours and 10 minutes. Going by train won't be that fast but you will get fares starting from ₹ 637.
The weather at Chennai is varying from "nice" to "hotter than nice".