  We address the existence and properties of solitons in thermal media with
periodic modulation of linear refractive index. Many kinds of solitons in such
optical lattices, including symmetric and antisymmetric lattices, are found
under different conditions. We study the influence of the refractive index
difference between two different layers on solitons. It is also found that
there do not exist cutoff value of propagation constant and soliton power for
shifted lattice solitons. In addition, the solitons launched away from their
stationary position may propagate without oscillation when the confinement from
lattices is strong.
