The Large UV/Optical/IR Surveyor (LUVOIR) is one of four Astro2020 Decadal Survey Missions, a concept for ‘flag-ship’ class space-borne observatory, operating across the multi-wavelength UV/Optical/NIR spectra. An Optical Telescope concept being considered is the segmented primary mirror architecture with composite backplane structure. In order to achieve the high-contrast imaging required to satisfy the primary science goals of this mission would require a pico-meter wavefront RMS stability over a wavefront control time step, a milli-Kelvin level thermometry sensing and control, and near-zero CTE materials. The LUVOIR primary mirror segment assemblies and composite backplane support structure require active thermal management to maintain operational temperature during flight operations. Furthermore, the active thermal control must be sufficiently stable to prevent time-varying thermally induced structure distortions to minimize optical aberrations. This paper describes a Thermal System Architecture of 2 concepts considered for the LUVOIR decadal study, and a systematic approach to developing a thermal architecture of modular composite sections of the mirror support structure and primary mirror segment assemblies.