We have studied the spatial and temporal distribution of abundances of chemical elements in large "gradual" solar energetic-particle (SEP) events, and especially the source plasma temperatures, derived from those abundances, using measurements from the Wind and Solar TErestrial RElations Observatory (STEREO) spacecraft, widely separated in solar longitude. A power-law relationship between abundance enhancements and mass-to-charge ratios [A/Q] of the ions can be used to determine Q-values and source plasma temperatures at remote spacecraft with instruments that were not designed for charge-state measurements. We search for possible source variations along the accelerating shock wave, finding one clear case where the accelerating shock wave appears to dispatch ions from 3.2±0.8 MK plasma toward one spacecraft and those from 1.6±0.2 MK plasma toward another, 116 o away. The difference persists three days and then fades away. Three other SEP events show less-extreme variation in source temperatures at different spacecraft, in one case observed over 222 o in longitude. This initial study shows how the power-law relation between abundance enhancements and ion A/Q-values provides a new technique to determine Q and plasma temperatures in the seed population of SEP ions over a broad region of space using remote spacecraft with instruments that were not originally designed for measurements of ionization states.