  A challenge in fundamental physics and especially in thermodynamics is to
understand emergent order in far-from-equilibrium systems. While at
equilibrium, temperature plays the role of a key thermodynamic variable whose
uniformity in space and time defines the equilibrium state the system is in,
this is not the case in a far-from-equilibrium driven system. When energy flows
through a finite system at steady-state, temperature takes on a
time-independent but spatially varying character. In this study, the convection
patterns of a Rayleigh-B{\'e}nard fluid cell at steady-state is used as a
prototype system where the temperature profile and fluctuations are measured
spatio-temporally. The thermal data is obtained by performing high-resolution
real-time infrared calorimetry on the convection system as it is first driven
out-of-equilibrium when the power is applied, achieves steady-state, and then
as it gradually relaxes back to room temperature equilibrium when the power is
removed. Our study provides new experimental data on the non-trivial nature of
thermal fluctuations when stable complex convective structures emerge. The
thermal analysis of these convective cells at steady-state further yield local
equilibrium-like statistics. In conclusion, these results correlate the spatial
ordering of the convective cells with the evolution of the system's temperature
manifold.
