In the case of a turbojet (with no "cold" bypass flow), the airflow being directed forward by an hypothetical thrust reverser can be really hot.
Depending on the location of the engine, this flow may be dangerously redirected towards the empennage and the fuselage.
For instance, for a fighter this would be a hazard for sensors, equipment, payloads including missiles, likely many other elements, and pilots:
General Dynamics F-16C (source: Wikipedia)
Are there turbojet engines fitted with a thrust reverser? Which aircraft are they used for? How is this problem dealt with?