The radiative recombination coefficientB, defined bydN/dt=dP/dt≡−BNP, of two‐dimensional free carriers,NandP, in a selectively doped GaAs/n‐Al0.3Ga0.7As quantum well was determined in the temperature rangeTbetween 15 and 300 K by measuring the decay time &tgr; of photoluminescence from the quantum well with electron densityN0=1×1012/cm2. It is found thatB(=1/&tgr;N0) is 1.1–1.9×10−4cm2/s at 300 K and increases asTis lowered, reaching 2.3×10−3cm2/s (&tgr;∼0.43 ns) at 15 K. The initial increase ofBis nearly proportional to 1/T, whereasBtends to saturate at low temperature. These experimental findings are shown to be well explained by the theory of band‐to‐band recombination of two‐dimensional carriers in quantum wells.