  The anomalous Hall and Nernst effects are considered theoretically within
Matsubara-Green's function formalism. The effective Hamiltonian of a magnetized
two-dimensional electron gas with cubic Rashba spin-orbit interaction may
describe transport properties of electronic states at the interfaces or
surfaces of perovskite oxides or another type of heterostructures that, due to
symmetry, may be described by the same effective model. In the quasi-ballistic
limit, both effects are determined by the topological (Fermi sea) contribution
whereas the states at the Fermi level gives a negligibly small response. For a
wide range of parameters describing the considered system, the anomalous Nernst
conductivity reveals a change of the sign before the magnetic phase transition.
