Gold neutral beam probes are used for the determination of the space potentials at the thermal barrier cells and the central cell of the GAMMA 10 tandem mirror. The thermal barrier potential is determined by simultaneous measurements of the on-axis space potentials at both locations. Equipotential contours over a cross-section at the barrier are measured by sweeping the probing beams with different beam energies. The enhancement of the thermal barrier depth and of the neoclassical radial ion transport in relation with two-dimensional space potential profiles has been studied in GAMMA 10 for the case of low density experiments.