We present results regarding the disc response functions and the corresponding time lags assuming a standard Novikov–Thorne accretion disc illuminated by a point-like X-ray source. We took into account all relativistic effects in the light propagation from the X-ray source to the disc and then to the observer, and we computed the disc reflection, accounting for its radial ionization profile. Our results suggest that the thermal reverberation effects should be stronger in sources with large X-ray source height and low accretion rate. We found that time lags increase with height and accretion rate. The amplitude of the observed time lags as a function of wavelength (in NGC 5548) is consistent with the model predictions. It is not necessary for the disc to be too hot, it may be that the X-ray source is located further from the disc.