  The effects of thermal convection on turbulence in accretion discs, and
particularly its interplay with the magnetorotational instability (MRI), are of
significant astrophysical interest. Despite extensive theoretical and numerical
studies, such an interplay has not been explored experimentally. We conduct
linear analysis of the azimuthal version of MRI (AMRI) in the presence of
thermal convection and compare the results with our experimental data published
before. We show that the critical Hartmann number ($Ha$) for the onset of AMRI
is reduced by convection. Importantly, convection breaks symmetry between $m =
\pm 1$ instability modes ($m$ is the azimuthal wavenumber). This preference for
one mode over the other makes the AMRI-wave appear as a ``one-winged
butterfly''.
