The aim of this paper is to study the influence of the measurement noise (on the flux) and of model bias on the temperature estimation by multispectral method with two, three or four colors using a model based on the Wien's approximation (and flux ratio) and taking into account spectral emissivity up to 2-order variations (a special case will be considered: variation according to the Drude's law). For this purpose, in a first part the model and the method will be presented, then in a second part, the estimation of parameters from a regularized nonlinear least squares regression algorithm (Levenberg-Marquardt), and their statistical properties obtained using a Monte Carlo method (1000 estimates) will be discussed. The study will conclude with experimental validations in the InfraRed range (using a thermal camera).