  Indefinite causal order is a key feature involved in the study of quantum
higher order transformations. Recently, intense research has been focused on
possible advantages related to the lack of definite causal order of quantum
processes. Quite often the quantum switch is claimed to provide advantages in
information-theoretic and thermodynamic tasks. We address here the question
whether indefinite causal order is a resource for quantum thermodynamics.
Inspired by previous results in the literature, we show that indefinite causal
order is not necessary for the reported increase in free energy and ergotropy.
More specifically, we show that a simple causally ordered process, which
replaces the system's state with a new one before the final measurement,
outperforms the quantum switch in all thermodynamic tasks considered so far. We
further show that a similar advantage can be also achieved without completely
discarding system, if we allow for non-Markovian interactions between the
system and an environment. We extend the analysis to more extreme examples of
indefinite causal order, showing that they do not provide an advantage either.
Finally, we discuss a possible way to study the advantages that may arise from
indefinite causal order in a general scenario.
