If you're flying, dont forget to keep a good book for company.
There are direct trains but no direct flights for this journey. Chennai (Tamil Nadu) to Jammu (Jammu And Kashmir) distance is 2754 km and you can get there by flight + flight in just over 6 hours and 55 minutes or by train fares starting from ₹ 723.
The heat there will make you sweat, but it's surely bearable.