We analyse the transient transmission response of a high quality (Q) factor whispering gallery mode resonator when the probe laser frequency is rapidly swept across the resonance. The detailed comparison with a simple numerical linear model allows the coupling regime and the strength of the intracavity Rayleigh scattering to be measured. By including thermal nonlinearities in the model we show here that it can be possible to deduce the power launched in the high-Q mode by using this simple cavity ring-down spectroscopy technique.