In this paper we propose an outlier detection algorithm for temperature sensor data from jet engine tests. Effective identification of outliers would enable engine problems to be examined and resolved efficiently. Outlier detection in this data is challenging because a human controller determines the speed of the engine during each manoeuvre. This introduces variability which can mask abnormal behaviour in the engine response. We therefore suggest modelling the dependency between speed and temperature in the process of identifying abnormalities. The engine temperature has a delayed response with respect to the engine speed, which we will model using robust functional regression. We then apply functional depth with respect to the residuals to rank the samples and identify the outliers. The effectiveness of the outlier detection algorithm is shown in a simulation study. The algorithm is also applied to real engine data, and identifies samples that warrant further investigation.