 Solution

A heat engine must reject some absorbed heat to a colder reservoir. For heat addition and rejection at absolute temperatures $T_h$ and $T_c$, the Carnot bound isAt fixed $T_c$, increasing $T_h$ increases this upper limit and can increase useful specific work in an appropriately designed gas-turbine cycle. Thus a higher hot-side temperature permits more efficient conversion of heat to work, rather than merely heating the exhaust. Real combustion occurs over a temperature range, and actual efficiency also depends on pressure ratio, losses and cycle design: peak temperature alone does not determine it. The materials incentive is to sustain higher turbine inlet temperatures while maintaining strength, oxidation resistance and acceptable creep life.