The effect of rotation on the boundary layers (BLs) in a Rayleigh–Bénard system at a relatively low Rayleigh number, i.e., Ra = 4×107, is studied for different Pr by direct numerical simulations and the results are compared with laminar BL theory. In this regime, we find a smooth onset of the heat transfer enhancement as function of increasing rotation rate. We study this regime in detail and introduce a model based on the Grossmann–Lohse theory to describe the heat transfer enhancement as function of the rotation rate for this relatively low Ra number regime and weak background rotation Ro¿1. The smooth onset of heat transfer enhancement observed here is in contrast to the sharp onset observed at larger Ra¿108 by Stevens et al. [Phys. Rev. Lett. 103, 024503 (2009)] , although only a small shift in the Ra-Ro-Pr phase space is involved.