I would add that if the transfer case clutch plates have slipped enough to burn the fluid (as you noted) then the plates themselves may be damaged as well. You may get away with just new fluid, or it may be the first indication of failing clutch plates. Time will tell.

__________________
2007 X3 3.0si, 6 MT, Premium, White

Retired:
2008 535i, 6 MT, M Sport, Premium, Space Grey
2003 X5 3.0 Steptronic, Premium, Titanium Silver
2002 325xi 5 MT, Steel Grey
2004 Z4 3.0 Premium, Sport, SMG, Maldives Blue