Wow ! I really wish I could come with you on this one.
There are direct flights and trains for this journey. Chennai (Tamil Nadu) to Bhubaneshwar (Orissa) distance is 1235 km and you can get there by flight in just over 2 hours and 55 minutes or by train fares starting from ₹ 445.
The weather at Bhubaneshwar is varying from "nice" to "hotter than nice".