The rheological behavior of an ionic liquid was investigated by means of molecular dynamics simulations with experimental contribution, under conditions close to those found in the elastohydrodynamic and the very-thin film lubrication regimes. The molecular model was applied to nearly 200 temperature–pressure–shear rate cases, without any parameter adjustment. Experiments were conducted on a rheometer and a high-pressure falling-body viscometer. This unique combination of numerical and experimental tools has enabled the full description of the ionic liquid rheological response to extreme conditions of temperature, pressure and shear rate. In the linear domain, a very good consistency between the two computational approaches (nonequilibrium molecular dynamics, equilibrium molecular dynamics via the Green–Kubo formalism) and the experiments was obtained on the Newtonian viscosity. Reliable values of the pressure–viscosity coefficient, another rheological characteristic necessary for predicting film thickness in the regimes of interest in this work, were inferred. Compared with a conventional lubricant of almost identical Newtonian viscosity, the pressure–viscosity coefficient of the ionic fluid is much lower, its variations with temperature remaining, however, very similar. The application of the time–temperature–pressure superposition principle and the regression to the Carreau equation for describing the nonlinear domain have revealed, for the first time, significant variations in the exponent of the Carreau model which have been correlated with the changes in temperature and pressure.