<p>Nowadays, heterogeneous distributed multiprocessor/multicore systems with an arbitrary network face a big challenge to conserve their high reliability when scheduling tasks with data dependencies, and that is due to the effects of temperature involved, energy consumed, and makespan needed to process these tasks without omitting the transient and permanent fault effects. In this paper, an efficient approach based static scheduling, called Fault tolerant Heuristic with high Reliability and low Temperature under controlled Energy and Makespan (FHRTEM) is proposed with the aim of keeping system in high reliability and low temperature without exceeding an energy consumption threshold and a given common deadline even in presence of transient or permanent faults using a sophisticated fitness function. For that, reliability is increased by adding replicas judiciously, temperature is reduced by using sleep/active technique alternatively, energy consumption is moderated by affecting low frequency for processor/core to manage primary(main tasks)/backup(replicas) using DVFS option, minimizing makespan is realized by affecting high frequency under transient and permanent faults. The fault tolerance is supported by a contingency schedule. The efficiency of FHRTEM is validated using real-world application graphs. The obtained results clearly show the superiority of FHRTEM over state-of-the-art approaches in terms of reliability and temperature.</p>