“It won’t melt because empty space has a very low conductivity”.
Sure, it won’t heat up by conduction. What kind of an explanation is this?
Useless. Heat in space is transferred by radiation, not conduction. If the argument were correct, all the planets would be frozen.
Only heat flux radiation matters to the heat shield. The shield is a black-body radiator, as reflective and emissive as possible, shading as much of the craft as possible. The shield is connected to the craft by struts with as little conductivity as possible, the gap allowing the back side of the shield to radiate away from the craft. Only conduction matters on the craft, which is liquid cooled, and is as actually as conductive as possible to protect the instruments.