Small object detection has been a classic problem in the field of infrared image processing, and the objects are usually brighter than the local background they are in. However, in some scenarios, the target brightness may be lower than the background brightness. For example, the civil aircrafts usually has low-temperature skin when cruising, appearing as dark points on medium spatial resolution thermal infrared satellite images. There are few features of these objects, so the current detection network structure has redundancy. Hence, we proposed a lightweight dark object detection network, AirFormer. It only has 37.1K parameters and 46.2M floating-point operations on a 256256 image. Considering the lack of infrared dark object detection dataset, we analyzed the characteristics of aircrafts on thermal infrared satellite images, and then developed a simulated flying aircraft detection dataset called IRAir. Our proposed AirFormer achieves 71.0% at recall and 82.6% at detection precision on the IRAir dataset. Based on simulated training data, AirFormer achieves detection of real flying aircrafts on the thermal infrared satellite images.