The Carnot efficiency is the maximum attainable efficiency in terms of extracting work from a temperature differential, not the actual efficiency in a turbine engine. For the actual efficiency, you should look into the Brayton cycle, which approximates a turbine engine much better.
With that out of the way, let's look at the Carnot cycle. This cycle assumes a heat source that can provide arbitrary amounts of energy at a certain temperature $T_h$, and a heat sink that can sink arbitrary amounts of heat at a temperature $T_c$. These are the isothermal parts of the cycle. To get the working fluid to either temperature, adiabatic compression is used.
These heat sources and sinks do not exist in reality, but by approximation, the atmosphere is an excellent heat sink, and burning fuel is an excellent heat source. The low temperature is thus taken as the atmospheric temperature which can be as low as -50°C (~220 K, remember that Carnot's efficiency is defined in terms of absolute temperature) and the high temperature is the temperature in the combustion chamber.
Sometimes you hear that $T_h$ is the hottest temperature in the cycle, and $T_c$ the coldest temperature. While this is often true in practice, this does not need to be the case for theoretical considerations. The only thing that matters for the Carnot efficiency is the temperature of the heat sinks/sources. You can't get more efficient than the Carnot cycle by hooking your engine up to a fridge. Indeed, the Carnot cycle is just a way to express the Second Law of Thermodynamics, which states that entropy in a closed system can never increase.
