This paper presents a fully-automated method to establish a calibration dataset from on-site scans and recalibrate the intrinsic parameters of a spinning multi-beam 3-D scanner. The proposed method has been tested on a Velodyne HDL-64E S2 LiDAR system, which contains 64 rotating laser rangefinders. By time series analysis, we found that the collected range data have random measurement errors of around ±25 mm. In addition, the layered misalignment of scans among the rangefinders, which is identified as a systematic error, also increases the difficulty to accurately locate planar surfaces. We propose a temporal-spatial range data fusion algorithm, along with a robust RANSAC-based plane detection algorithm to address these issues. Furthermore, we formulate an alternative geometric interpretation of sensory data using linear parameters, which is advantageous for the calibration procedure. The linear representation allows the proposed method to be generalized to any LiDAR system that follows the rotating beam model. We also confirmed in this paper, that given effective calibration datasets, the pre-calibrated factory parameters can be further tuned to achieve significantly improved performance. After the optimization, the systematic error is noticeable lowered, and evaluation shows that the recalibrated parameters outperform the factory parameters with the RMS planar errors reduced by up to 49%.