For a spatial modulation of the control parameter which describes, for instance, major effects of a rough container boundary in Rayleigh-Benard convection, the threshold value of the bifurcation from a homogeneous basic state to a spatially periodic state is provided analytically and numerically, taking the one-dimensional cubic-quintic complex Ginzburg-Landau equation with real coefficients as an example. Above the threshold, using the Poincare-Lindstedt expansion, we show that the quintic term affects both the stationary nonlinear solution and the Nusselt number. (C) 2016 Elsevier Ltd. All rights reserved.