Excellent question Louise
The fuel efficiency of an aeroplane engine depends on:
– how much of the energy of the incoming air gets used by the engine rather than being carried away as wasted kinetic energy. So you want to make sure the speed of the air coming out from the exhaust of the engine is the same as the speed of the air going into the front (so that no kinetic energy is lost)
– how efficiently the engine can accelerate the aeroplane. This is where the temperature is important. You need to have a really high temperature in the combustor to be able to efficiently accelerate the flow of air going out the exhaust of the engine (which will accelerate the aeroplane).
This combustion temperature is limited in modern engines by the melting temperature of the metal parts in the turbine. This is why we use advanced materials (like ceramics) and good cooling systems that can keep the surface of the metal parts at a safe temperature while still being able to have a high combustion temperature to increase the efficiency of the engine.