  The shear-current effect in a nonrotating homogeneous turbulent convection
with a large-scale constant shear is studied. The large-scale velocity shear
causes anisotropy of turbulent convection, which produces the mean
electromotive force $\bec{\cal E}^{(W)} \propto {\bf W} {\bf \times} {\bf J}$
and the mean electric current along the original mean magnetic field, where
${\bf W}$ is the background mean vorticity due to the shear and ${\bf J}$ is
the mean electric current. This results in a large-scale dynamo even in a
nonrotating and nonhelical homogeneous sheared turbulent convection, whereby
the $\alpha$ effect vanishes. It is found that turbulent convection promotes
the shear-current dynamo instability, i.e., the heat flux causes positive
contribution to the shear-current effect. However, there is no dynamo action
due to the shear-current effect for small hydrodynamic and magnetic Reynolds
numbers even in a turbulent convection, if the spatial scaling for the
turbulent correlation time is $\tau(k) \propto k^{-2}$, where $k$ is the
small-scale wave number.
