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In this paper, we consider the Bayesian Cramer-Rao bound (BCRB) for the dynamical estimation of multi-path Rayleigh channel complex gains in data-aided (DA) and non-data-aided (NDA) OFDM systems. This bound is derived in an on-line and off-line high Doppler scenarios for time-varying complex gains within one OFDM symbol, assuming the availability of prior information. In NDA context, whereas this true BCRB is hard to evaluate, we present a closed-form expression of a BCRB, i.e., the Modified BCRB (MBCRB). We discuss, based on the theoretical and simulation results, the benefit of using the a priori information and, the past and the future observations for the complex gains estimation.