Signaling overhead reduction has been a key approach to realizing energy-efficient wireless cooperative communication systems. Motivated by the fact that consecutive temporal samples of real-world wireless channels are typically correlated, this paper proposes to exploit such time-domain correlation for relay training overhead reduction in cooperative networks. Specifically, we consider a cooperative transmit beamforming system, in which relay terminals employing the decode-and-forward protocol collaboratively transmit the source message according to the pre maximal-ratio-combining (pre-MRC) principle. During the training phase, the relays send training signals to aid channel estimation at the destination. Based on the acquired record of the channel state information (CSI), the destination then employs a linear minimum-mean-square-errors (LMMSE) channel predictor to update the CSI; in this way, training overhead dedicated by relays can then be reduced. We derive a closed-form expression for the receive SNR at the destination when the pre-MRC beamforming factors are computed in accordance with the predicted CSI. Our analytic results can be used for characterizing the performance degradation of channel prediction as the duration of the prediction phase is enlarged. The proposed analytic studies are corroborated by numerical simulations.