The present publication is concerned with the study of thermodynamic properties of a quantum mechanical system composed of a small particle system (such as a spin chain) and several quantized massless boson fields (as photon gasses or phonon fields) at positive temperature. As the text at hand is a contribution to the area of mathematical physics it unites mathematical concepts of the thermodynamics of a quantum system with the mathematically rigorous treatment of problems in positive temperature quantum physics. The dissertation character of this publication is reflected by the fact that recent research work of the author is displayed along with a review of established results in the field of statistical quantum mechanics. An extended introductory part serves as thorough familiarization of non-experts with the field of studies. The required technical tools for the mathematical treatment of the system under consideration are carefully compiled apart from the main text.