The third harmonic extraordinary (X3) mode of electron cyclotron emission is investigated, aiming at its diagnostic capability towards the measurement of electron temperature, Te, of plasmas with higher densities exceeding the second harmonic extraordinary (X2) mode cutoff. A Bayesian data-analysis approach is adopted through the forward modeling of the X3 emission observations to extract the underlying Te profile. Bayesian analysis shows that the high field side of the X3 emission spectrum is sufficient to provide the Te profile. Additionally, for plasma control purposes, a correction factor is provided to track continuous core Te from the measured radiation temperature of the optically grey X3 emission.