  In the classical world, physical events always happen in a fixed causal
order. However, it was recently revealed that quantum mechanics allows events
to occur with indefinite causal order (ICO). In this study, we use an optical
quantum switch to experimentally investigate the application of ICO in
thermodynamic tasks. Specifically, we demonstrate that when a working system
interacts with two thermal reservoirs in an ICO, non-classical heat transfer
can be observed, even through they share the same temperature. Using such a
process, we simulate an ICO refrigeration cycle and investigate its properties.
We also show that by passing through the ICO channel multiple times, one can
extract more heat per cycle and thus obtain a higher refrigeration efficiency.
Our results provide inspirations for further improving the efficiency of
quantum thermodynamic tasks and shed new light on the development of a new
class of thermodynamic resource theories without presumed causal order.
