Temporal graph regression is a frequently encountered research problem in many studies of graph analytics. A temporal graph is a sequence of attributed graphs where node features and target variables change over time, but network structure stays constant. The task of temporal graph regression is to predict the target variables associated with nodes at future time-points given historical snapshots of the graph. Existing methods tackle this problem mostly by conducting structured regression for all target variables. However, those methods have limited performance due to redundant information. Although several techniques have been proposed recently to learn lower dimensional embedding for the target space, the problem of how to effectively exploit the structure of the temporal graph in such embeddings is still unsolved. Other recent works only study node embedding of the stationary graphs only, and this is not applicable to temporal attributed graphs. In this paper, we introduced a Structure-Aware Intrinsic Representation Learning model (SAIRL) to jointly learn lower dimensional embeddings of the target space and feature space via structure-aware graph abstraction and feature-aware target embedding learning. To solve this problem, we have developed a derivative-free block coordinate descent algorithm with closed-form solutions. To characterize the quality of embedding-based learned with SAIRL, we conducted extensive experiments on a variety of different real-world temporal graphs. The results indicate that the proposed method can be more accurate than the state-of-the-art embedding learning methods, regardless of regressors.