Dual-task dialog language understanding aims to tackle two correlative dialog language understanding tasks simultaneously via leveraging their inherent correlations. In this paper, we put forward a new framework, whose core is relational temporal graph reasoning. We propose a speaker-aware temporal graph (SATG) and a dual-task relational temporal graph (DRTG) to facilitate relational temporal modeling in dialog understanding and dual-task reasoning. Besides, different from previous works that only achieve implicit semantics-level interactions, we propose to model the explicit dependencies via integrating prediction-level interactions. To implement our framework, we first propose a novel model Dual-tAsk temporal Relational rEcurrent Reasoning network (DARER), which first generates the context-, speaker- and temporal-sensitive utterance representations through relational temporal modeling of SATG, then conducts recurrent dual-task relational temporal graph reasoning on DRTG, in which process the estimated label distributions act as key clues in prediction-level interactions. And the relational temporal modeling in DARER is achieved by relational graph convolutional networks (RGCNs). Then we further propose Relational Temporal Transformer (ReTeFormer), which achieves fine-grained relational temporal modeling via Relation- and Structure-aware Disentangled Multi-head Attention. Accordingly, we propose DARER with ReTeFormer (DARER 2), which adopts two variants of ReTeFormer to achieve the relational temporal modeling of SATG and DTRG, respectively. The extensive experiments on different scenarios verify that our models outperform state-of-the-art models by a large margin. Remarkably, on the dialog sentiment classification task in the Mastodon dataset, DARER and DARER 2 gain relative improvements of about 28% and 34% over the previous best model in terms of F1.