For applications in robotics and autonomous vehicles, fusing 3D LiDAR, RGB camera, and thermal camera can improve the perception in day and night environments. To fuse the sensors, accurate extrinsic calibration is important. However, most existing methods use offline calibration, which is tedious, as it requires the use of special targets and human intervention. Meanwhile, among the online calibration methods, little attention has been paid to LiDAR and thermal camera online calibration. Thus, in this paper, an online extrinsic calibration method is proposed to solve the problem, called RGBDTCalibNet. It can achieve the extrinsic calibration between a 3D LiDAR and an RGB camera, as well as a 3D LiDAR and a thermal camera. It leverages CNN-based deep learning methods for feature extraction and feature matching. The proposed network only takes a pair of images and point cloud as the input and outputs the extrinsic parameters in a single shot. It is trained and tested on two datasets: KITTI360 and our own dataset collected in the NTU campus, using two types of LiDAR: Velodyne HDL-64 and Livox Horizon. Both demonstrate the effectiveness, robustness and accuracy of RGBDTCalibNet. The code will be open-sourced at https://github.com/sanatmharolkar/RGBDTCalibNet.git