Photoluminescence upconversion removes energy from the medium. It has been applied extensively for laser cooling of atomic vapors and more recently also to condensed matter, such as dye solutions and glasses. The application to semiconductors has also been proposed, but so far, clear evidence is missing. We present a detailed experimental study of photoluminescence upconversion in GaAs quantum wells. We study the conversion efficiency over a wide temperature range as a function of the laser detuning. The best results are obtained when the laser detuning is comparable to the thermal energy, $2{k}_{B}T$.