We describe an analysis procedure for estimating the thermospheric winds and temperatures from the multi-order two-dimensional (2D) interferograms produced by an imaging Fabry–Perot interferometer (FPI) as imaged by a CCD detector. We also present a forward model describing the 2D interferograms. To investigate the robustness and accuracy of the analysis, we perform several Monte Carlo simulations using this forward model for an FPI that has recently been developed and deployed to northeastern Brazil. The first simulation shows that a slight cross-contamination at high temperatures exists between neighboring orders in the interferogram, introducing a bias in the estimated temperatures and increasing errors in both the estimated temperatures and winds when each order is analyzed in full. The second simulation investigates how using less than an entire order in the analysis reduces the cross contamination observed in the first set of simulations, improving the accuracy of the estimated temperatures. The last simulation investigates the effect of the signal-to-noise ratio on the errors in the estimated parameters. It is shown that, for the specific FPI simulated in this study, a signal-to-noise ratio of 1.5 is required to obtain thermospheric wind errors of $5\mathrm{m}/\mathrm{s}$ and temperature errors of $20\mathrm{K}$ .