Profiles of the plasma electron temperature Te and density ne are routinely determined on JET with the LIDAR Thomson Scattering (TS) system. Although the system is robust and produces data for all plasma discharges independent of plasma parameters (e.g. field, current, density) the signal to noise performance is below modern expectations. The approach used so far for Te and ne measurement is based on log-linear or non-linear fit of the experimentally-obtained, relativistically-thermally-broadened lidar-return spectra to the corresponding theoretical expression. Recently we developed two novel complimentary approaches for determination of Te on the basis of an analysis of the relativistic TS spectrum and estimated analytically their potential accuracies. The methods are based on the unambiguous temperature dependence, respectively, of the Center-of-Mass Wavelength (CMW) of the LIDAR-return spectrum and of the ratio of the signal powers of two spectral regions. The main purpose of the present work is to perform thorough simulations of the determination of electron temperature by the CMW method and to estimate accurately the measurement error as a function of Te and the Signal-to-Noise Ratio (SNR).