To test whether the interface between an Fe-alloy electrode and a SrTiO3 (STO) tunnel barrier constitutes or not a good spin injector, we have studied the transport and magnetic properties of CoFe2 (7.5 nm)/SrTiO3 (3 nm)/CoFe2 (1 nm)/NiFe (8 nm) stacks prepared by pulsed-laser deposition on STO(001) substrates and varied the STO barrier deposition temperature. While this parameter does not strongly influence the magnetic properties of the two electrodes, the resulting barrier height at the bottom CoFe2/STO interface is lowered if the STO barrier is deposited at 300 degrees C rather than 80 degrees C and an already low-tunnel-magnetoresistance ratio is suppressed. We discuss our findings in terms of the oxide stability of the CoFe2/STO interface.