  Context. Comparison studies of Sun-like stars with the Sun suggest an
anomalously low photometric variability of the Sun compared to Sun-like stars
with similar magnetic activity. Comprehensive understanding of stellar
variability is needed, to find a physical reasoning for this observation. Aims.
We investigate the effect of metallicity and effective temperature on the
photometric brightness change of Sun-like stars seen at different inclinations.
The considered range of fundamental stellar parameters is sufficiently small so
the stars, investigated here, still count as Sun-like or even as solar twins.
Methods. To model the brightness change of stars with solar magnetic activity,
we extend a well established model of solar brightness variations, SATIRE
(which stands for Spectral And Total Irradiance Reconstruction), which is based
on solar spectra, to stars with different fundamental parameters. For that we
calculate stellar spectra for different metallicities and effective temperature
using the radiative transfer code ATLAS9. Results. We show that even a small
change (e.g. within the observational error range) of metallicity or effective
temperature significantly affects the photometric brightness change compared to
the Sun. We find that for Sun-like stars, the amplitude of the brightness
variations obtained for Str\"omgren (b + y)/2 reaches a local minimum for
fundamental stellar parameters close to the solar metallicity and effective
temperature. Moreover, our results show that the effect of inclination
decreases for metallicity values greater than the solar metallicity. Overall,
we find that an exact determination of fundamental stellar parameters is
crucially important for understanding stellar brightness changes.
