  We investigate electric polarizations emergent perpendicular to an applied
thermal gradient in insulating systems. The thermally-induced electric
polarization, known as thermopolarization, has been studied conventionally in
the case that an electric polarization appears along the thermal gradient.
Here, we focus on the antisymmetric component of the thermopolarization tensor
and reveal that it becomes nonzero owing to the ferro-type order for
electric-toroidal dipole moments. To describe local electric polarizations
originating from the disproportionation of localized electronic clouds, we
introduce a two-dimensional three-orbital model with localized $s$ and two $p$
orbitals, where the electric polarization at each site interacts with the
neighboring one as dipole-dipole interactions. We find that a vortex-type
configuration of local electric polarizations appears as a mean-field ground
state, corresponding to a ferro-type electric-toroidal dipole order. By taking
account of collective modes from this ordered state, we calculate the
coefficient of the thermopolarization based on the linear response theory. The
antisymmetric component is nonzero in the presence of the electric-toroidal
dipole order. We clarify that fluctuations in the $p$ orbitals are crucial in
enhancing the antisymmetric thermopolarization. We discuss the appearance
conditions based on the symmetry argument and the relevance to real materials.
