We report a continuous wave room temperature quantum cascade laser operating in an external cavity in the Littrow configuration with a 10-facet polygon mirror rotating at 24,000 RPM. The quantum cascade laser emission is swept across ∼1520 - 1625 cm-1 wavenumber range in less than ∼45 µs with a sweep repetition rate of 4 kHz. The measured maximum output power at the laser gain maximum, 15°C and 0.86 A driving current is ∼90 mW; the estimated average output power across the 45 µs wavenumber sweep is ∼50 mW. Through its sweep, the laser emits on the sequential Fabry-Perot longitudinal modes of the laser chip cavity with the mode separation of ∼0.5 cm-1. The linewidth of the emitting modes is less than ∼0.05 cm-1. Spectral measurements of the infrared absorption features of a 10 µm thick layer of acetophenone and water vapor in the air have demonstrated the capability of obtaining spectral data in less than 45 µs.