Heterogeneous Vehicular Networks (HetVNets) play a key role by stacking different communication technologies such as sub-6GHz, mm-wave and DSRC to meet diverse connectivity needs of 5G/B5G vehicular networks. HetVNet helps address the humongous user demands-but maintaining a steady connection in a highly mobile, real-world conditions remain a challenge. Though there has been ample of studies on beam prediction models a dedicated solution for HetVNets is sparsely explored. Hence, it is the need of the hour to develop a reliable beam prediction solution, specifically for HetVNets. This paper introduces a lightweight deep learning-based solution termed-"CAR-BRAINet" which consists of convolutional neural networks with a powerful multi-head attention (MHA) mechanism. Existing literature on beam prediction is largely studied under a limited, idealised vehicular scenario, often overlooking the real-time complexities and intricacies of vehicular networks. Therefore, this study aims to mimic the complexities of a real-time driving scenario by incorporating key factors such as prominent MAC protocols-3GPP-C-V2X and IEEE 802.11BD, the effect of Doppler shifts under high velocity and varying distance and SNR levels into three high-quality dynamic datasets pertaining to urban, rural and highway vehicular networks. CAR-BRAINet performs effectively across all the vehicular scenarios, demonstrating precise beam prediction with minimal beam overhead and a steady improvement of 17.9422% on the spectral efficiency over the existing methods. Thus, this study justifies the effectiveness of CAR-BRAINet in complex HetVNets, offering promising performance without relying on the location angle and antenna dimensions of the mobile users, and thereby reducing the redundant sensor-latency.