Recently, the growing demand for autonomous driving in the industry has led to a lot of interest in 3D object detection, resulting in many excellent 3D object detection algorithms. However, most 3D object detectors focus only on a single set of LiDAR points, ignoring their potential ability to improve performance by leveraging the information provided by the consecutive set of LIDAR points. In this paper, we propose a novel 3D object detection method called temporal motion-aware 3D object detection (TM3DOD), which utilizes temporal LiDAR data. In the proposed TM3DOD method, we aggregate LiDAR voxels over time and the current BEV features by generating motion features using consecutive BEV feature maps. First, we present the temporal voxel encoder (TVE), which generates voxel representations by capturing the temporal relationships among the point sets within a voxel. Next, we design a motion-aware feature aggregation network (MFANet), which aims to enhance the current BEV feature representation by quantifying the temporal variation between two consecutive BEV feature maps. By analyzing the differences and changes in the BEV feature maps over time, MFANet captures motion information and integrates it into the current feature representation, enabling more robust and accurate detection of 3D objects. Experimental evaluations on the nuScenes benchmark dataset demonstrate that the proposed TM3DOD method achieved significant improvements in 3D detection performance compared with the baseline methods. Additionally, our method achieved comparable performance to state-of-the-art approaches.