In recent years, the performance of deep neural networks (DNNs) is significantly improved, making them suitable for many application fields, such as autonomous driving, advanced robotics, and industrial control. Despite a lot of research being devoted to improving the accuracy of DNNs, only limited efforts have been spent to enhance their timing predictability, required in several real-time applications. This paper proposes a software infrastructure based on the Linux operating system to integrate DNNs within a real-time multicore system. It has been realized by modifying both the internal scheduler of the popular TensorFlow framework and the SCHED_DEADLINE scheduling class of Linux. The proposed infrastructure allows providing timing isolation of DNN inference tasks, hence improving the determinism of the temporal interference generated by TensorFlow. The proposal is finally evaluated with a case study derived from a state-of-the-art benchmark inspired by an autonomous industrial system. Extensive experiments demonstrate the effectiveness of the proposed solution and show a significant reduction of both average and longest-observed response times of TensorFlow tasks.