Nice ! Looks like you're all set for your vacation ?
There are direct trains but no direct flights for this journey. Chennai (Tamil Nadu) to Haridwar (Uttarakhand) distance is 2390 km and you can get there by flight + cab in just over 9 hours and 41 minutes or by train fares starting from ₹ 675.
The heat there will make you sweat, but it's surely bearable.