Automaton based approaches have enabled robots to perform various complex tasks. However, most existing automaton based algorithms highly rely on the manually customized representation of states for the considered task, limiting its applicability in deep reinforcement learning algorithms. To address this issue, by incorporating Transformer into reinforcement learning, we develop a Double-Transformer-guided Temporal Logic framework (T2TL) that exploits the structural feature of Transformer twice, i.e., first encoding the LTL instruction via the Transformer module for efficient understanding of task instructions during the training and then encoding the context variable via the Transformer again for improved task performance. Particularly, the LTL instruction is specified by co-safe LTL. As a semantics-preserving rewriting operation, LTL progression is exploited to decompose the complex task into learnable sub-goals, which not only converts non-Markovian reward decision processes to Markovian ones, but also improves the sampling efficiency by simultaneous learning of multiple sub-tasks. An environment-agnostic LTL pre-training scheme is further incorporated to facilitate the learning of the Transformer module resulting in an improved representation of LTL. The simulation results demonstrate the effectiveness of the T2TL framework.