The absorption spectra of exhaust gases (H2O, CO, CO2, NO, NO2, and SO2) and aerosol (soot and Al2O3) particles were modeled at different temperatures for the first time and suitable spectral ranges were determined for conducting laser remote sensing of the combustion products of jet engines. The calculations were conducted on the basis of experimental concentrations of the substances and the sizes of the aerosol particles. The temperature and geometric parameters of jet engine exhausts were also taken from the literature. The absorption spectra were obtained via the line-by-line method, making use of the spectral line parameters from the authors' own high-temperature databases (for NO2 and SO2 gases) and the HITEMP 2010 database, and taking into account atmospheric transmission. Finally, the theoretical absorption spectra of the exhaust gases were plotted at temperatures of 400, 700, and 1000 K, and the impact of aerosol particles on the total exhaust spectra was estimated in spectral ranges suitable for remote sensing applications.