Best method to loosen and remove stuck brass nut?

If you want to go the heat/shrink route, this is how I would approach it. The nut is part of the tube (soldered to the tube. You should heat the ring below the nut. Then rapidly cool down the tube with the nut. I would cool it from the inside of the tube. This will shrink the tube while the ring and the tank will retain most of the heat and remain expanded.

Brgds,
E.Fuhrmeister

 

That's not entirely correct. Parts attached to the stove tanks, like pump tubes, legs, the bottom plate etc., are generally soldered with a pretty soft, low temp soldering, so these things can come loose by mistake pretty easily if caution not is taken.

 

This for reference:
http://www.engineeringtoolbox.com/thermal-expansion-metals-d_859.html

Most copper based metals expand quite a lot.

Brgds,
E.Fuhrmeister