Privacy-preserving distributed beamforming designs are conceived for temporally correlated vector parameter estimation in an orthogonal frequency division multiplexing (OFDM)-based wireless sensor network (WSN). The temporal correlation inherent in the parameter vector is exploited by the rate distortion theory-based bit allocation framework used for the optimal quantization of the sensor measurements. The proposed distributed beamforming designs are derived via fusion of the dual consensus alternating direction method of multiplier (DC-ADMM) technique with a pertinent privacy-preserving framework. This makes it possible for each sensor node (SN) to design its transmit precoders in a distributed fashion, which minimizes the susceptibility of vital information to malicious eavesdropper (Ev) nodes, while simultaneously avoiding the significant communication overhead required by a centralized approach for the transmission of the state information to the fusion center (FC). The Bayesian Cramer-Rao bound (BCRB) is derived for benchmarking the estimation performance of the proposed transmit beamformer and receiver combiner designs, while our simulation results illustrate the performance and explicitly demonstrate the trade-off between the privacy and estimation performance.