Anyway, I'd read a description (apparently mistaken) somewhere listing Aqua Fortis as Nitric acid.
Not mistaken but one of the points of confusion - in the old days pure nitric acid was known as Aqua Fortis, later the ferric nitrate mix made by dissolving iron in nitric acid was also called Aqua Fortis.
If you make your own aquafortis and make sure that the acid can't dissolve any more iron, it shouldn't need neutralizing because all of the acid should be used up in the reaction.
Your right it shouldn't but even the commercially prepared (almost pure) Ferric Nitrate crystals available from scientific supply companies require neutralizing or the stock will darken.
an example - the piece on the left was neutralized only on the top - notice how the vertical face is much darker due to not being neutralized and then exposed to the sun:
re: heat - the major reason is to make any remaining nitric acid more volatile so it will off gas.
You can get virtually the same effect as Aqua Fortis aka ferric nitrate with ferric acetate, iron dissolved in vinegar, but due to the higher volatility of the acetic acid in vinegar there is no need to heat or neutralize.
Some examples of both Ferric Nitrate and Ferric Acetate:
The top piece was done with some old Wahkon Bay AF as a control. On the lower piece three different mixes were used:
left - ferric acetate aka iron dissolved in vinegar
center - commercially prepared ferric nitrate crystals dissolved in distilled water which "makes" Aqua Fortis; they are available from the Science Company and other suppliers
right - ferric nitrate aka Aqua Fortis made by dissolving degreased steel wool in a bottle of Birchwood Casey Plum Brown, which is 10% nitric plus other acids (if you do this do it OUTSIDE with PLENTY of ventilation and in a large Pyrex bowl along with chemical rubber gloves, eye protection, and a good mask).
All pieces of wood were finished with a homemade period linseed oil based varnish.