The extraction of Brainstem Auditory Evoked Potentials (BAEPs), from the EEG background, is of high clinical interest. The present paper can be considered as a continuation of our previous work related to the BAEP estimation in endocochlear pathologies. In our previous published work, we proposed a technique for time delay estimation on the basis of the BAEPs in response to successive stimulations. Put in a different manner, our objective was the estimation of the dynamics of the cochlea that is responsible for the delayed responses. The estimation technique was based on optimization of a non-linear criterion by means of Simulated Annealing Time Delay Estimation (SATDE) algorithm. However, it is well known that such heuristic algorithms are time consuming and largely depend on the number of parameters to be estimated. The present paper demonstrates that modeling the non-stationarity of responses considerably decreases the convergence time to the global minimum. The newly proposed method in this paper, called Fast Simulated Annealing Time Delay Estimation (FSATDE) algorithm, has been validated on both simulated and real signals.