Wow ! I really wish I could come with you on this one.
There are direct trains but no direct flights for this journey. Chennai (Tamil Nadu) to Jammu (Jammu And Kashmir) distance is 2755 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 temperatures at this time of the day are in a comfortable range.