A mathematical model of an ideal observation thermal imager (TI) is developed. At designing of model it was supposed: (1) The main noise source is a shot noise of photons irradiating a photosensitive element (PSE) of TI. (2) Temperature and reflection coefficients of objects under observation differ a little from the corresponding performances of the scence (background radiation). (3) Luminescence of the image of a local object area (LA) on a display screen of TI (useful signal) is determined by the difference between the electric charge accumulated in the canal PSE (optically conjugate with this local sites) and electric charge, accumulated in PSE canal, optically conjugated with the science. It was taken into account in the model: quantum efficiency of PSE, accumulation time in the PSE canal, the format of the array and PSE, parameters of a lens, losses in optical elements, mean temperatures and reflection (radiance) coefficients of the scene, temperatures and reflection (radiance)LA, counterradiation of the environment. Calculations (with consideration of counterradiation, angular sizes of objects, performances of objects and the scene) of utmost signal-noise ratio's; radiation noise equivalent temperature difference (NETD); radiation noise equivalent of reflection coefficients difference (NERD) for two spectral ranges: 3-5 μm and 8-14 μm. The quantitative evaluations of the influence of performances of environment on the listed above utmost parameters of TI for observation are obtained.