We address the problem of estimating atmosphere parameters (temperature, water vapour content) from data captured by an airborne thermal hyperspectral imager, and propose a method based on direct optimization. The method also involves the estimation of object parameters (temperature and emissivity) under the restriction that the emissivity is constant for all wavelengths. Certain sensor parameters can be estimated as well in the same process. 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. More than 20 bands does not improvethe estimates. The proposedmethod is alsoextended to incorporateadditionalknowledge,for examplemeasurements ofatmospheric parameters and sensor noise.