Nice ! Looks like you're all set for your vacation ?
There are direct trains but no direct flights for this journey. Catching a flight is the fastest way to do this journey. Direct trains are available as well. kolkata (West Bengal) to Haridwar (Uttarakhand) distance is 1503 km and you can get there by flight + cab in just over 9 hours and 11 minutes. Going by train won't be that fast but you will get fares starting from ₹ 499.
The heat there will make you sweat, but it's surely bearable.