A self-consistent many-body theory is developed to study the effect of temperature and electron density on the interband absorption coefficient and the frequency-dependent refractive index for an array of isolated quantum wires. The peaks in the absorption coefficient correspond to interband transitions resulting in the resonant absorption of light. The oscillations in the derivative spectrum are due to the quantization of the energy levels related to the in-plane confining potential for such reduced dimensional systems. There are appreciable changes in the absorption spectrum when the electron density or temperature is increased. One interband transition peak is suppressed in the high electron density limit and the thermal depopulation effect on the electron subbands can be easily seen when the temperature is high. We also find that the exciton coupling weakens the shoulder features in the absorption spectrum. This study is relevant to optical characterization of the confining potential and the areal density of electrons using photoreflectance. By using incident light with tunable frequencies in the interband excitation regime, contactless photoreflectance measurements may be carried out and the data compared with our calculations. By fitting the numerical results to the peak positions of the photoreflectance spectrum, the number of electrons in each wire may be extracted.