  We demonstrate that the supercurrent can be strongly enhanced in cross-like
superconducting hybrid nanostructures (X-junctions) exposed to a temperature
gradient. At temperatures T exceeding the Thouless energy of our X-junction the
Josephson current decays algebraically with increasing T and can be further
enhanced by a proper choice of the circuit topology. At large values of the
temperature gradient the non-equilibrium contribution to the supercurrent may
become as large as the equilibrium one at low T. We also predict a variety of
transitions between 0- and $\pi$-junction states controlled by the temperature
gradient as well as by the system geometry. Our predictions can be directly
verified in modern experiments.
