This paper considers the stability of the one-dimensional boundary layer ge
nerated by sudden heating of an infinite vertical wall. A quasi-steady appr
oximation is used to obtain the asymptotic form of the growth rate and phas
e speed of disturbances whose wavelength is comparable with the boundary-la
yer width. Results for the inviscid modes governed by Rayleigh's equation a
re obtained for several values of the Prandtl number and are compared with
solutions of the full stability equations. As the wavelength increases, the
phase speed of disturbances approaches the maximum flow speed of the bound
ary layer and a five-tier structure extends across and outside the boundary
layer. This intermediate regime, where viscous effects are important withi
n a critical layer centred on the position of maximum flow speed, provides
a link with an earlier long-wave analysis of the problem.