  The suppression of high-$p_\perp$ particles is one of the main signatures of
parton energy loss during its passing through the QGP medium, and is reasonably
reproduced by different theoretical models. However, a decisive test of the
reliability of a certain energy loss mechanism, apart from its path-length, is
its temperature dependence. Despite its importance and comprehensive dedicated
studies, this issue is still awaiting for more stringent constraints. To this
end, we here propose a novel observable to extract temperature dependence
exponent of high-$p_{\perp}$ particle's energy loss, based on $R_{AA}$. More
importantly, by combining analytical arguments, full-fledged numerical
calculations and comparison with experimental data, we argue that this
observable is highly suited for testing (and rejecting) the long-standing
$\Delta E/E \propto L^2 T^3$ paradigm. The anticipated significant reduction of
experimental errors will allow direct extraction of temperature dependence, by
considering different centrality pair in $A + A$ collisions (irrespective of
the nucleus size) in high-$p_\perp$ region. Overall, our results imply that
this observable, which reflects the underlying energy loss mechanism, is very
important to distinguish between different theoretical models.

Nuclear Theory;High Energy Physics - Phenomenology