In recent years, vehicular communication has attracted significant research attention for its potential as a fifth generation (5G) application. The IEEE 802.11p standard enables the wireless technology that defines vehicular communication and, due to the time-varying characteristic, one of its critical challenges is to ensure communication reliability. Moreover, this standard is based on orthogonal frequency division multiplexing (OFDM) transmission scheme, which may suffer from nonlinear distortions induced by high power amplifiers (HPA) at the transmitter, degrading the channel estimation and detection performance of the receivers. In this work, the application of deep learning (DL) based channel estimation schemes to the IEEE 802.11p standard in presence of HPA distortions is presented. Simulation results show that the deep neural network (DNN) based estimation schemes outperform conventional data-pilot aided (DPA) and spectral temporal averaging (STA) estimators in terms of bit error rate and normalized mean squared error, evidencing their superiority in providing reliable estimation in mobility scenarios in presence of HPA nonlinear distortions. Furthermore, the hybrid solution, employing a joint DNNbased post-processing and conventional estimation, achieves less computational complexity than the DL-based proposal on top of the initial DPA estimation.