Internet of Things (IoT) applications generate tremendous amounts of data streams which are characterized by varying Quality of Service (QoS) indicators. These indicators need to be accurately estimated in order to appropriately schedule the computational and communication resources of the access and Edge networks. Nonetheless, such types of IoT data may be produced at irregular time instances, while suffering from varying network conditions and from the mobility patterns of the edge devices. At the same time, the multipurpose nature of IoT networks may facilitate the co-existence of diverse applications, which however may need to be analyzed separately for confidentiality reasons. Hence, in this paper, we aim to forecast time series data of key QoS metrics, such as throughput, delay, packet delivery and loss ratio, under different network configuration settings. Additionally, to secure data ownership while performing the QoS forecasting, we propose the FeDerated Temporal Sparse Transformer (FeD-TST) framework, which allows local clients to train their local models with their own QoS dataset for each network configuration; subsequently, an associated global model can be updated through the aggregation of the local models. In particular, three IoT applications are deployed in a real testbed under eight different network configurations with varying parameters including the mobility of the gateways, the transmission power and the channel frequency. The results obtained indicate that our proposed approach is more accurate than the identified state-of-the-art solutions.