The excitonic population lifetime and its temperature dependence is measured in nanometer-scale quantum wires. The measurements were performed on two cleaved-edge overgrown GaAs quantum-wire systems, in which the lateral dimensions are comparable to the dimensions of a reference quantum well and an easy comparison between them is straightforward. The excitonic population decay time in the wires is less sensitive to temperature changes than that in the wells. Whereas the latter is linear with temperature, the former is roughly proportional to the square root of the temperature. Consequently, the decay times of the photoluminescence from the wires are longer than those from the wells at low temperature, but shorter at higher temperatures. From the temperature dependence of the lifetimes, which is an unambiguous signature of a one-dimensional system, we find the intrinsic radiative lifetime of excitons in quantum wires. They are an order of magnitude longer than in quantum wells.