In an HX thruster, liquid propellant is pressure- or pump-fed to a lightweight planar heat exchanger. For orbital launch, the propellant of choice is liquid hydrogen. H2 provides a vacuum Isp of 600 seconds, sufficient for a robust single-stage-to-orbit capability, at a heat exchanger temperature of only 1000 C (less than 2000 F). The heat exchanger can therefore be made of ordinary materials, rather than exotic high-temperature alloys, which allows building cheap expendable vehicles.
This report is about laser heat exchanger launch system but should be valid. Dr. Kare has studied both laser and microwave launch systems. A single-stage-to-orbit vehicle does not shed tanks or stages. When it reenters the atmosphere is it a big empty tub with a very low cross-sectional mass density. The temperatures it encounters are dramatically lower than a capsule or the shuttle.
In other words, this is far from being the most difficult part of the system.