The photoluminescence of In0.4Ga0.6As quantum dots was investigated by scanning-near-field optical microscopy at temperatures between 300 and 4 K. Using etched, metal-coated fiber tips, the pure signal of individual quantum dots could be detected. The spectra are found to consist of Lorentzian-shaped emission lines with linewidths ranging from 10 to 20 meV at room temperature, reducing to less than the spectrometer resolution of 1 meV at 4 K. This behavior is in contrast to the expectation of extremely small linewidths amounting to a few mu eV, and can be related to lifetime effects mediated by thermal excitation of the carriers in the dots. Furthermore, the spectra show a redshift by about 8 meV upon increasing the excitation intensity, indicating biexcitonic effects.