Indeed, it is complicated.
Of course, there are more than one heat inleak to the LN. Although I would like to define what is the conduction through the rod which, as you can see, is cooling by the vapours. The rod is on one side at 300K and on the other at 77K. The vapours on the outlet are at 290K. Tomorrow, I can give you the mass flow. But now, we can assume 0.8g/s.