We address the problem of estimating atmosphere parameters (temperature, water vapor content) from data captured by an airborne thermal hyperspectral imager, and propose a method based on linear and non-linear optimization.The method is used for estimation of the parameters (temperature and emissivity) of the observed object, as well as for sensor gain under certain restrictions. The method is analyzed with respect to sensitivity to noise and number of spectral bands. Simulations with synthetic signatures are performed to validate the analysis, showing that estimation can be performed with as few as 10-20 spectral bands at moderate noise levels. The proposed method is also extended to exploit additional knowledge, for example measurements of atmospheric parameters and sensor noise. Additionally, we show how to extend the method in order to improve spectral calibration.