Temporal heterogeneous networks (THNs) are evolving networks that characterize many real-world applications such as citation and events networks, recommender systems, and knowledge graphs. Although different Graph Neural Networks (GNNs) have been successfully applied to dynamic graphs, most of them only support homogeneous graphs or suffer from model design heavily influenced by specific THNs prediction tasks. Furthermore, there is a lack of temporal heterogeneous networked data in current standard graph benchmark datasets. Hence, in this work, we propose DURENDAL, a graph deep learning framework for THNs. DURENDAL can help to easily repurpose any heterogeneous graph learning model to evolving networks by combining design principles from snapshot-based and multirelational message-passing graph learning models. We introduce two different schemes to update embedding representations for THNs, discussing the strengths and weaknesses of both strategies. We also extend the set of benchmarks for TNHs by introducing two novel high-resolution temporal heterogeneous graph datasets derived from an emerging Web3 platform and a well-established e-commerce website. Overall, we conducted the experimental evaluation of the framework over four temporal heterogeneous network datasets on future link prediction tasks in an evaluation setting that takes into account the evolving nature of the data. Experiments show the prediction power of DURENDAL compared to current solutions for evolving and dynamic graphs, and the effectiveness of its model design.