Nonequilibrium molecular dynamics (NEMD) simulations play a major role in characterizing the rheological properties of fluids undergoing shear flow. However, all previous studies of flows in molecular fluids either use an "atomic" thermostat which makes incorrect assumptions concerning the streaming velocity of atoms within their constituent molecules, or they employ a center of mass kinetic (COM) thermostat which only controls the temperature of relatively few degrees of freedom (3) in complex high molecular weight compounds. In the present paper we show how recently developed configurational expressions for the thermodynamic temperature can be used to develop thermostatting mechanisms which avoid both of these problems. We propose a thermostat based on a configurational expression for the temperature and apply it to NEMD simulations of decane undergoing Couette flow at constant volume and at constant pressure. The results so obtained are compared with those obtained using a COM kinetic thermostat. At equilibrium the properties of systems thermostatted in the two different ways are of course equivalent. However, we show that the two responses differ far from equilibrium. In particular, we show that the increase in the potential energy of the internal modes with increasing shear is only observed with a Gaussian isokinetic COM thermostat in both NVT and NPT simulations. There is no such increase with the configurational thermostat, which, unlike the Gaussian isokinetic COM thermostat, correctly accounts for the internal degrees of freedom of the molecular fluid.