To protect the inflatable structure even more from the heat of atmospheric flight NASA uses high-tech insulation as part of the thermal protection system. Think of the thermal protection system as an out-of-this-world version of a fireman's suit or a thermal blanket for a huge cone.
NASA's HIAD team is looking at all sorts of materials than can be combined together in layers to come up with the best, most heat resistant design. Usually, the thermal protection system is made up of an outer layer than can take the high heat; middle layers that insulate and keep the inflatable structure cooler; and one last layer of defense - a gas barrier - that keeps the hot gases from reaching the inflatable structure.
A combination of materials with names like Nextel, Pyrogel and Kapton are being used on one HIAD concept, the Inflatable Reentry Vehicle Experiment. The goal is to allow the heat shield to survive an atmospheric entry of up to 2,300 degrees Fahrenheit (1260 degrees Celsius).
That's hot -- but taken as a whole not as hot as a traditional rigid metal heat shield. Specific locations on a flexible heat shield don't get as hot as they do on current spacecraft aeroshells because an inflatable is so much larger in diameter it slows down earlier and the heat is spread over a larger surface area.