The transcriptional regulatory network (TRN) is a graph framework that helps understand the complex transcriptional regulation mechanisms in the transcription process. Identifying the phenotype-specific transcription regulators is vital to reveal the functional roles of transcription elements in associating the specific phenotypes. Although many methods have been developed towards detecting the phenotype-specific transcription elements based on the static TRN in the past decade, most of them are not satisfactory for elucidating the phenotype-related functional roles of transcription regulators in multiple levels, as the dynamic characteristics of transcription regulators are usually ignored in static models. In this study, we introduce a novel framework called DTGN to identify the phenotype-specific transcription factors (TFs) and pathways by constructing dynamic TRNs. We first design a graph autoencoder model to integrate the phenotype-oriented time-series gene expression data and static TRN to learn the temporal representations of genes. Then, based on the learned temporal representations of genes, we develop a statistical method to construct a series of dynamic TRNs associated with the development of specific phenotypes. Finally, we identify the phenotype-specific TFs and pathways from the constructed dynamic TRNs. Results from multiple phenotypic datasets show that the proposed DTGN framework outperforms most existing methods in identifying phenotype-specific TFs and pathways. Our framework offers a new approach to exploring the functional roles of transcription regulators that associate with specific phenotypes in a dynamic model.