Beyond 5G and 6G networks are expected to support new and challenging use cases and applications that depend on a certain level of Quality of Service (QoS) to operate smoothly. Predicting the QoS in a timely manner is of high importance, especially for safety-critical applications as in the case of vehicular communications. Although until recent years the QoS prediction has been carried out by centralized Artificial Intelligence (AI) solutions, a number of privacy, computational, and operational concerns have emerged. Alternative solutions have surfaced (e.g. Split Learning, Federated Learning), distributing AI tasks of reduced complexity across nodes, while preserving the privacy of the data. However, new challenges rise when it comes to scalable distributed learning approaches, taking into account the heterogeneous nature of future wireless networks. The current work proposes DISTINQT, a novel multi-headed input privacy-aware distributed learning framework for QoS prediction. Our framework supports multiple heterogeneous nodes, in terms of data types and model architectures, by sharing computations across them. This enables the incorporation of diverse knowledge into a sole learning process that will enhance the robustness and generalization capabilities of the final QoS prediction model. DISTINQT also contributes to data privacy preservation by encoding any raw input data into highly complex, compressed, and irreversible latent representations before any transmission. Evaluation results showcase that DISTINQT achieves a statistically identical performance compared to its centralized version, while also proving the validity of the privacy preserving claims. DISTINQT manages to achieve a reduction in prediction error of up to 65% on average against six state-of-the-art centralized baseline solutions presented in the Tele-Operated Driving use case.