One unresolved question in the high-temperature superconductors and their copper oxide parent compounds is the absence of a Cu2+ electron-spin-resonance (ESR) signal even at temperatures well above the Néel temperature. We have extended the measurements up to 1150 K in both single crystals and ceramic pellets of La2CuO4+, 00.12, and no ESR signal has been observed. Our data are not compatible with the models based only on magnetic fluctuations which predict an ESR linewidth of a few hundred Oe at such high temperatures. Other suggested explanations for the absence of a Cu2+ ESR signal are discussed. © 1993 The American Physical Society.