Consider the NS eqns for a system varying only in 1D, say d/dx is non zero.  
g=0.  Write down this system and confirm that for this 1D assumption uy and uz 
decouple from n, p, and ux.  For this system, we know that its linearized 
version includes sound waves and the entropy mode if ux is nonzero.  Thus, this 
system includes both these waves (in the NS description of course).  Further we 
know that the sound frequency will be very large compared with the entropy mode 
w since w for the latter is almost zero.

Start with this 1D system and obtain reduced (nonlinear) equations from it 
(lowest order only) by assuming that we are interested only in subsonic 
phenomena, ie, d/dt << cs/L, and u << cs, where cs is the sound speed.  For the 
NS system, lambda << L by definition.  Your final reduced system should be one 
single NL equation for T(x,t).  n can be eliminated and ux(x,t) can be written 
as an indefinite integral in terms of T(x,t).