This article concerns flight speed estimation from airflow measurements provided by a set of thermal anemometers. Our approach relies on a Gated Recurrent Unit (GRU) based deep learning approach to extract deep features from noisy and turbulent measurement signals of triaxial thermal anemometers, in order to establish the underlying mapping between the airflow measurement and the flight speed. The proposed solution is validated on a multi-rotor micro aerial vehicle (MAV). The results show that the GRU-based model can effectively extract noise features and perform denoising, and compensate for induced velocity effects along the propellers' rotation axis. As a consequence, robust prediction of the flight speed is performed, including during takeoff and landing that induce ground effects and strong variations of vertical airflow.