= 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 is
$$
\eta\le1-\frac{T_c}{T_h}.
$$
At fixed $T_c$, increasing $T_h$ increases this upper limit and can increase useful specific work in an appropriately designed gas-turbine cycle. Thus \b[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 (deformation)> life.
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