The ferroelectric semiconductor alpha-SnTe has been regarded as a topological crystalline insulator, and the dispersion of its surface states has been intensively measured with angle-resolved photoemission spectroscopy (ARPES) over the past decade. However, much less attention has been given to the impact of the ferroelectric transition on its electronic structure, and in particular on its bulk states. Here, we investigate the low-energy electronic structure of alpha-SnTe with ARPES and follow the evolution of the bulk-state Rashba splitting as a function of temperature, across its ferroelectric critical temperature of about T-c approximate to 110 K. Unexpectedly, we observe a persistent band splitting up to room temperature, which is consistent with an order-disorder contribution of local dipoles to the phase transition that requires the presence of fluctuating dipoles above T-c. We conclude that no topological surface state can occur under these conditions at the (111) surface of SnTe, at odds with recent literature.