In the realm of fully autonomous drones, the accurate detection of obstacles is paramount to ensure safe navigation and prevent collisions. Among these challenges, the detection of wires stands out due to their slender profile, which poses a unique and intricate problem. To address this issue, we present an innovative solution in the form of a monocular end-to-end model for wire segmentation and depth estimation. Our approach leverages a temporal correlation layer trained on synthetic data, providing the model with the ability to effectively tackle the complex joint task of wire detection and depth estimation. We demonstrate the superiority of our proposed method over existing competitive approaches in the joint task of wire detection and depth estimation. Our results underscore the potential of our model to enhance the safety and precision of autonomous drones, shedding light on its promising applications in real-world scenarios.