We present the results of a statistical study on high-level (above -200V in magnitude) negative-voltage spacecraft charging in eclipse at geosynchronous altitudes. Theoretically, there exists a critical temperature T* for a surface material. Below T*, no spacecraft charging occurs. Since T* depends on the surface material, which differs from satellite to satellite, each is expected to have its own critical temperature. The theoretical results are compared with the coordinated space-environmental parameter data obtained by the Los Alamos National Laboratory (LANL) geosynchronous satellites. The LANL data include spacecraft charging events measured on several geosynchronous satellites, in eclipse and in sunlight, over several years. We have found a nearly linear trend, or better described by a quadratic one, between the spacecraft potential and the ambient electron temperature for potentials below in magnitude of about -5 kV. Extrapolation of the linear trend to zero volts shows an intercept at a finite temperature which agrees reasonably well with the critical temperature predicted by theory. The existence of a critical electron temperature is useful for informing decision and operational support of geosynchronous spacecraft with enhanced knowledge.