Using a recent linear scaling method that fully accounts for anharmonic thermal vibrations, we calculated the activation free energy for {101¯2} twin boundary migration in magnesium up to 450 K, under both resolved shear stresses and non-glide stresses resulting from c-axis tension. Comparing to direct molecular dynamics data, we show that the harmonic transition state theory unexpectedly overestimates the activation entropy above temperatures as low as 100 K, leading to underestimates of the nucleation time by many orders of magnitude. Whilst a specific interface is studied, anharmonic and non-glide effects are expected to be generally significant in thermally activated interface migration. Anharmonic vibrational effects are shown to affect the kinetics of thermally activated processes even at low temperatures, which in the present case leads to an unexpected decrease in the nucleation rate.