In the present article, we have analyzed to which extent the steady states produced in simulations of fluids undergoing shear flow, can truly be representations of experimental steady states. For this purpose, we have performed nonequilibrium molecular dynamics (NEMD) simulations of two different fluid systems undergoing shear how. One system is a Lennard-Jones (LJ) fluid where the viscous heat produced by shearing the system is eliminated only in certain regions of the simulation box. The other system is a polymer immersed in an atomic solvent. In this case, the viscous heat was removed by coupling a homogeneous thermostat to different degrees of freedom in the system. The results of these simulations show that at the shear rates commonly produced in simulation, the rate of production of viscous heat is very large. This heat is eliminated by the thermostat at rates that are higher than the rates of transport of heat across the fluid. Moreover, the heat has no time to redistribute into the different degrees of freedom of the system, and different steady states are reached depending on to which degrees of freedom the thermostat is coupled. As a conclusion of this investigation we believe that the efforts of simulating fluids undergoing shear flow should be directed to simulate lower shear rates.