  Measurements and calculations have shown significant disagreement regarding
the sign and variations of the thermal expansion coefficient (TEC) of graphene
$\alpha(T)$. Here we report dedicated Raman scattering experiments conducted
for graphene monolayers deposited on silicon nitride substrates and over the
broad temperature range 150--900~K. The relation between those measurements for
the G band and the graphene TEC, which involves correcting the measured signal
for the mismatch contribution of the substrate, is analyzed based on various
theoretical candidates for $\alpha(T)$. Contrary to calculations in the
quasiharmonic approximation, a many-body potential reparametrized for graphene
correctly reproduces experimental data. These results indicate that the TEC is
more likely to be positive above room temperature.
