To achieve satisfactory performance in vehicle-to-everything (V2X) communications, it is paramount to accurately estimate the channel. The traditional data-pilot aided (DPA) scheme and the variation of DPA, e.g., spectral temporal averaging (STA), have been adopted for IEEE 802.11p due to their low complexity, but their performances are not satisfactory. The more recently proposed time domain reliable test frequency domain interpolation (TRFI) scheme only marginally improves the performance. Deep neural network (DNN)-based estimators, e.g., STA-DNN and TRFI-DNN, have substantially improved the channel estimation, and the long short-term memory (LSTM)-based estimators, such as LSTM-DPA-TA and LSTM-MLPDPA, achieve the state-of-the-art performance. LSTM-based estimators, however, have high computational complexity. In this paper, we propose a novel channel estimator that leverages temporal convolutional networks (TCNs) combined with the DPA procedure to estimate and track channel variations. Simulations on realistic V2X scenarios show that the proposed TCN-DPA channel estimation scheme outperforms existing methods in almost all V2X scenarios. The proposed estimator has about one order of magnitude improvement in terms of bit error rate compared to LSTM-based estimators. By exploiting the parallelism inherent in the TCN architecture, the computational complexity of the proposed TCN-DPA estimator is 40% and 47% lower than LSTM-DPA-TA and LSTM-MLP-DPA, respectively. Moreover, the training time of TCN-DPA is only 52% and 42% of the time of LSTM-DPA-TA and LSTM-MLP-DPA, respectively.