We report on the electrical transport properties of all-oxide La0.7Ca0.3MnO3/SrTiO3:Nb heterojunctions with lateral size of just a few micrometers. The use of lithography techniques to pattern manganite pillars ensures perpendicular transport and allows exploration of the microscopic conduction mechanism through the interface. From the analysis of the current-voltage characteristics in the temperature range 20-280 K we find a Schottky-like behavior that can be described by a mechanism of thermally assisted tunneling if a temperature-dependent value of the dielectric permittivity of SrTiO3:Nb (NSTO) is considered.We determine the Schottky energy barrier at the interface, qVB = 1.10 ± 0.02 eV, which is found to be temperature independent, and a value of ? = 17 ± 2 meV for the energy of the Fermi level in NSTO with respect to the bottom of its conduction band.