You're embarking on an interesting journey!
There are direct trains but no direct flights for this journey. Travelling by train is the cheapest way of getting there. kolkata (West Bengal) to Rishikesh (Uttarakhand) distance is 1523 km and you can get there by train in just over 32 hours and 48 minutes. However, flight + cab tickets come also cheap with fares starting from ₹ 7911.
The temperatures at this time of the day are in a comfortable range.