Type-r,Welcome to the City of Joy--Kolkata.
By 1730HRS it will be almost dark here,but it will not be so cold here.
From which station will you board train for Patna---Howrah or Sealdah??
Both stations are a bit far from the airport,Dum Dum area.It will take more or less 1hr-1n1/2hrs to reach any of them ,depending on the traffic conditions.
Are you going by your own private vehicle??If not then there are other options like prepaid cab services, Rental Car services and AC Bus services.All of them are inside the Subhash Chandra Bose International Airport Terminal--SCBIAT.
Have a pleasant stay over here and enjoy.
Hope we could meet, but our schedules will not match as you said