Hmm .. that journey is surely more than just a weekend trip ?
There are direct trains but no direct flights for this journey. Mumbai (Maharashtra) to Rishikesh (Uttarakhand) distance is 1659 km and you can get there by flight + train in just over 8 hours and 17 minutes or by train fares starting from ₹ 536.
The heat there will make you sweat, but it's surely bearable.