Hmm .. that journey is surely more than just a weekend trip ?
There are direct flights and trains for this journey. Catching a direct flight is the fastest way to do this journey. Direct trains are available as well. kolkata (West Bengal) to Goa (Goa) distance is 2125 km and you can get there by flight in just over 4 hours and 5 minutes. Going by train won't be that fast but you will get fares starting from ₹ 633.
The temperatures at this time of the day are in a comfortable range.