In this work, we discuss recent developments in the computer simulations of molecular fluids under thermal gradients. Non-equilibrium simulations allow performing numerical tests of fundamental questions of non-equilibrium thermodynamics. These tests show that non-equilibrium simulations provide an efficient approach to quantify within a single simulation the thermophysical properties of fluids along an isobar. We discuss aspects connected to the computation of local temperatures in systems under the influence of heat fluxes, and how the combination of non-equilibrium molecular dynamics and non-equilibrium thermodynamics allows understanding phenomena arising from the coupling of internal molecular variables and heat fluxes, which lead, e.g. to thermo-molecular orientation. The behavior of these orientational effects near a fluid critical point is also discussed.
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