Although satisfiability checking is known to be an effective approach in classical planning, it has scarcely been investigated in the field of temporal planning. Most notably, the usage of E-step semantics for encoding the problem into a SAT formula, while being demonstrably quite efficient for decreasing the size of the encodings in classical planning, has not yet been employed to tackle temporal planning problems. In this paper, we define temporal versions of classical A-step and E-step plans. We show that when the casual and temporal reasoning phases of a SAT-based temporal planner are separated, these semantics can be used to translate a given temporal planning problem into a SAT formula. We introduce two different types of E-step encodings in temporal planning. The first encoding method is a temporal version of the classical E-step encoding. Like its classical counterpart, in the new encoding we suppose a few restrictive simplifying assumptions. On the other hand, by relaxing one of these assumptions, the second type of E-step encodings, which is often more compact than the first one, is introduced. However, if a temporal planning problem possesses the property that we call required causal simultaneity, neither of our proposed encodings will be expressive enough to represent a valid temporal plan. Nevertheless, we show that this property is rather rare and can be detected in polynomial time. Our experiments indicate that by embedding the proposed encodings into ITSAT, a SAT-based temporal planner based on the A-step encoding, a considerable improvement is achieved in terms of both speed and memory usage of the planner. The resulting planner significantly outperforms POPF, which is currently the state-of-the-art of temporally expressive planners.