  The release of causal structure of physical events from a well-defined order
to an indefinite one stimulates remarkable enhancements in various quantum
information tasks. Some of these advantages, however, are questioned for the
ambiguous role of the control system in the quantum switch that is an
experimentally realized process with indefinite causal structure. In
communications, for example, not only the superposition of alternative causal
orders, but also the superposition of alternative trajectories can accelerate
information transmissions. Here, we follow the proposal of Liu et al. [Phys.
Rev. Lett. 129, 230604 (2022)], and examine the information enhancement effect
of indefinite causal orders with the toolkit of thermodynamics in a photonic
platform. Specifically, we simulate the thermal interaction between a system
qubit and two heat baths embedded in a quantum switch by implementing the
corresponding switched thermal channels. Although its action on the system
qubit only is thermally free, our results suggest that the quantum switch
should be seen as a resource when the control qubit is also considered.
Moreover, we characterize the non-Markovian property in this scenario by
measuring the information backflows from the heat baths to the system qubit.
