Through the analysis of peak broadening of energy-dispersive diffraction lines from a powdered sample, the yield strength of alpha-Si3N4 was investigated at a pressure of 9 GPa and temperatures up to 1234 degrees C. During compression at room temperature, the lattice strain deduced from peak broadening increased linearly with pressure up to 9.2 GPa, with no clear indication of strain saturation. While heating at 9 GPa, diffraction peaks narrowed and significant stress relaxation was observed at temperatures above 400 degrees C, indicating the onset of yielding. The yield strength of alpha-Si3N4 decreases rapidly with increasing temperature: from 8.7 GPa at 400 degrees C to 4.0 GPa at 1234 degrees C. The low temperature for the onset of yielding and decrease of yield strength upon further heating bring up concern regarding the performance of alpha-Si3N4 as an engineering material. Finally, the grain size variation is also outlined together with the dependence of differential strain on pressure and on temperature. This provides crucial information for clarifying the "fine structure" of the evolution of the differential strain.