A road trip to Odisha in May. Torrid temperatures spiced up with Indian elections. I must say, it sounds daunting. I would urge all sensible precautions: plenty of hydration, cooling fruit, hats and doing indoors-y stuff during the day as far as possible.
Your journey to Odisha is best done via Kurnool on the smooth NH 40. Head east after that, where Vijayawada can be your first night halt. From there, along the eastern coast of Andhra to Gopalpur should take you close to 13 hours. For your travel within Odisha, it makes sense to use a few cities or towns as your base as you explore the surrounding areas. A rough itinerary would touch Gopalpur–Chilika– Bhubaneswar (with day trips to Udaygiri, Khandagiri and Dhauli)–Puri (with day trips to Konark and Satapada)–Cuttack (with a trip to Paradeep)– Daringbadi via scenic Phulbani.
This itinerary should roughly cover everything the state has to offer: temples, history, architecture, culture, beaches, scenic beauty, waterfalls, Irrawaddy dolphins, birding, forests and wildlife. You can leave Odisha via Gopalpur again, returning the way you came, or alternatively, bearing west from Arakku to Bhadrachalam. Circle the outer roads of Hyderabad and zip back to Bengaluru via Kurnool again. Possible night stops are Bhadrachalam and Kurnool. Now, you have rationed Rs 10,000 per day for four persons for your trip. This is doable but it necessitates sacrificing a little on stay options. There are budget options everywhere, and it’s worth your while to explore hotels that suit your sensibilities and wallet. See orissatourism.org for a list. Also try Odisha Tourism Development Corporation’s (OTDC) list of properties at panthanivas.com. They are moderately priced and have hotels in almost every spot along the itinerary you are looking for.