How do we manage such extreme conditions? There are a number of different strategies, and two of them aren’t so different from your own body’s way of handling heat…
The first, called a heat sink, could be considered the “toughing it out” approach; here, you construct your R/V of a material that can soak up the heat you’re experiencing along the way without experiencing structural failure along the way. This particular strategy was used on the North American Aviation X-15 rocket plane. It used a “hot structure” that could tolerate the heat load it experienced under normal conditions.
The second, ablation, is analogous to sweating. Rather than relying on insulation, ablation absorbs energy from the airstream by making it work to do another task - pyrolysing (burning) an expendable heat shield. The phase change effectively removes energy from the proximity of the vehicle. Ablation can be used in conjunction with other heat management methods; in fact, a number of ablative coatings were used on and tested with the X-15 during its program lifespan.
The third, radiation, relies on emitting heat back into the atmosphere at a faster rate than it is absorbed. This strategy is used to an extent on the Space Shuttle - the black tiles are very efficient at both absorption and radiation, allowing the bottom of the Orbiter to get rid of some of the intense heat of re-entry. As mentioned before, some vehicles use multiple approaches - the Shuttle itself uses both # 1 & 3, while the X-15 (during a part of the program) used # 1 & 2. There are other ways to manage heat, as well.