Deep learning has emerged as an effective solution for solving the task of object detection in images but at the cost of requiring large labeled datasets. To mitigate this cost, semi-supervised object detection methods, which consist in leveraging abundant unlabeled data, have been proposed and have already shown impressive results. However, most of these methods require linking a pseudo-label to a ground-truth object by thresholding. In previous works, this threshold value is usually determined empirically, which is time consuming, and only done for a single data distribution. When the domain, and thus the data distribution, changes, a new and costly parameter search is necessary. In this work, we introduce our method Adaptive Self-Training for Object Detection (ASTOD), which is a simple yet effective teacher-student method. ASTOD determines without cost a threshold value based directly on the ground value of the score histogram. To improve the quality of the teacher predictions, we also propose a novel pseudo-labeling procedure. We use different views of the unlabeled images during the pseudo-labeling step to reduce the number of missed predictions and thus obtain better candidate labels. Our teacher and our student are trained separately, and our method can be used in an iterative fashion by replacing the teacher by the student. On the MS-COCO dataset, our method consistently performs favorably against state-of-the-art methods that do not require a threshold parameter, and shows competitive results with methods that require a parameter sweep search. Additional experiments with respect to a supervised baseline on the DIOR dataset containing satellite images lead to similar conclusions, and prove that it is possible to adapt the score threshold automatically in self-training, regardless of the data distribution.