Thermal conductivity of low-density materials in thermal insulation systems varies dramatically with the environment: cold vacuum pressure, residual gas composition, and boundary temperatures. Using a reference material of aerogel composite blanket (reinforcement fibers surrounded by silica aerogel), an experimental basis for the physical heat transmission model of aerogel composites and other low-density, porous materials is suggested. Cryogenic-vacuum testing between the boundary temperatures of 78 K and 293 K is performed using a one meter cylindrical, absolute heat flow calorimeter with an aerogel blanket specimen exposed to different gas environments of nitrogen, helium, argon, or CO2. Cold vacuum pressures include the full range from 1x10(-5) ton to 760 ton. The soft vacuum region, from about 0.1 ton to 10 ton, is complex and difficult to model because all modes of heat transfer - solid conduction, radiation, gas conduction, and convection - are significant contributors to the total heat flow. Therefore, the soft vacuum tests are emphasized for both heat transfer analysis and practical thermal data. Results for the aerogel composite blanket are analyzed and compared to data for its component materials. With the new thermal conductivity data, future applications of aerogel-based insulation systems are also surveyed. These include Mars exploration and surface systems in the 5 ton CO2 environment, field joints for vacuum-jacketed cryogenic piping systems, common bulkhead panels for cryogenic tanks on space launch vehicles, and liquid hydrogen cryofuel systems with helium purged conduits or enclosures.