We have studied the cyclotron decay time of a Landau-quantized two-dimensional electron gas as a function of temperature (0.4-100 K) at a fixed magnetic field (±1.25T) using terahertz time-domain spectroscopy in a gallium arsenide quantum well with a mobility of μdc=3.6×106cm2V-1s-1 and a carrier concentration of ns=2×1011cm-2. We find a cyclotron decay time that is limited by superradiant decay of the cyclotron ensemble and a temperature dependence that may result from both dissipative processes as well as a decrease in ns below 1.5K. Shubnikov-de Haas characterization determines a quantum lifetime, τq=1.1ps, which is significantly faster than the corresponding dephasing time, τs=66.4ps, in our cyclotron data. This is consistent with small-angle scattering as the dominant contribution in this sample, where scattering angles below θ≤13 do not efficiently contribute to dephasing. Above 50K, the cyclotron oscillations show a strong reduction in both the oscillation amplitude and lifetime that result from polar optical phonon scattering.