Bjorn is correct in stating that compressor exit temperature T3 can be a limiting factor, just like turbine rotor inlet temperature T4.1, low rotor speed N1, and high rotor speed N2.
The response of the engine control system when reaching one of these limits is to stop increasing core fuel flow, or reduce fuel flow as necessary to keep at or below the limit. This reduces the aerodynamic rotor speed of the engine, reducing airflow, pressure ratio, and thrust. In supersonic flight, increasing inlet temperature with greater speed causes all these parameters to increase until one of them hits its limit (called the Theta break), with increasing inlet temperature causing loss of engine performance beyond that point. The total propulsion system performance can continue to increase with inlet ram recovery multiplying the engine pressure ratio for greater nozzle pressure ratio, but the engine contribution decreases beyond that limit condition.