The behavior of simple fluids under shear is investigated using molecular dynamics simulations. The simulated system consists of a fluid confined between two atomistic walls which are moved in opposite directions. Two approaches for shear flow simulations are compared: in one case, the sheared fluid is not thermostatted and only the confining walls are maintained at a constant temperature, while in the other, a thermostat is employed to keep the entire mass of the sheared fluid at a constant temperature. In the first case the sheared fluid undergoes significant viscous heating at the shear rates investigated, consistent with experimental observations and with theoretical predictions. Most simulations to date, however, have used the second approach which is akin to studying a fluid with infinite thermal conductivity. It is shown here that results for transport coefficients are significantly affected by the thermostat; in fact, the transport properties of the fluid determined using the two methods exhibit a qualitatively different shear rate dependence. It is also shown that the temperature profiles observed in our simulations can be described by continuum mechanics, provided the temperature dependence of the viscosity and thermal conductivity is taken into account.