Gas turbine hot component failures often cause catastrophic consequences. Fault detection can improve the availability and economy of hot components. The exhaust gas temperature (EGT) profile is usually used to monitor the performance of the hot components. The EGT profile is uniform when the hot component is healthy, whereas hot component faults lead to large temperature differences between different EGT values. The EGT profile swirl under different operating and ambient conditions also cause temperature differences. Therefore, the influence of EGT profile swirl on EGT values must be eliminated. To improve the detection sensitivity, this paper develops a fault detection method for hot components based on a convolutional neural network (CNN). This paper demonstrates that a CNN can extract the information between adjacent EGT values and consider the impact of the EGT profile swirl. This paper reveals, in principle, that a CNN is a viable solution for dealing with fault detection for hot components. Based on the distribution characteristics of EGT thermocouples, the circular padding method is developed in the CNN. The sensitivity of the developed method is verified by real-world data. Moreover, the developed method is visualized in detail. The visualization results reveal that the CNN effectively considers the influence of the EGT profile swirl.