Temperatures in the thermosphere (the region between 85 - 500 km above the earth's surface) can reach up to 1200 degrees Celsius. It therefore seems reasonable that a space ship traveling through that region would be severely damaged or "blow up". However, space ships use heat shields that prevent this from happening.

Heat shields are made of a variety of materials that can withstand extremely high temperatures (for example ceramics or metals), and thus protect the space ship from burning up upon re-entry into the atmosphere. The specifics in terms of which material is used depend on whether or not the heat tiles need to be re-used, and what the exact temperatures are that they need to endure. Sometimes ablating heat tiles are used, which get charred and partially burn off into the atmosphere.

Pictures and descriptions of some of the material used for heat shields can be found on the NASA web page:
Superhero Ceramics!
X-33 metallic heat shield