The study of the temperature dependence of Raman spectrum of graphene quantum dots is important for further understanding of the fine structure and properties of the material such as atomic bonds, thermal expansion, and thermal conductivity. In this work, we present new results on the temperature dependence of the frequency of G peak in the Raman spectra of bare GQDs and nitrogen-doped graphene quantum dots (N-GQDs), respectively. The nature of these GQDs is investigated using high-resolution transmission electron microscopy together with Raman, absorption, and photoluminescence spectra. We monitored a shift in G peak frequency toward lower frequencies with the temperature ranging from 81 to 663 K. In addition, a slight decrease in G peak intensity and an increase in D peak intensity have been observed, which is especially clear for Raman spectra of N-GQD sample. From the linear relationship of G peak frequency with temperature, we determine for the first time the value of the temperature coefficient chi of the G mode. Values of - 0.0222 +/- 0.001 cm(-1) K-1 for GQDs, and - 0.0243 +/- 0.0013 cm(-1) K-1 for N-GQDs were deduced. These results show a clear heat expansion in the graphene lattice, although small in size, when sample temperature is increased from 81 to 663 K. Our result is important to further understand physical effects induced by anharmonic phonons in QGDs and should be taken to account when designing efficient nanoelectronic devices employing GQDs.