The Jones matrix based polarimetric method suitable for the spatially resolved analysis of the thermally induced birefringence and dichroism in complex high-power laser optical systems is proposed. The measurement allows the characterization of the complete local Jones matrix of the optical components, or their sets. The method of extraction of the particular contributions of the linear and circular birefringence and dichroism is also suggested in order to recognize the phenomena and effects contributing to the total induced polarization state distortions. The whole procedure is demonstrated on the simulated experiment which analyses a very general inhomogeneous polarization distorting piece of material.