Jet engines work at a higher temperature that the melting point of Titanium Superalloy so how do they not melt?
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Turbine blades are usually some Nickel based superalloy (particularly the high pressure turbines). Believe it or not they aren’t the most thermally stressed portion, that honor goes to the hot spots on the stator. That is the non rotating ‘blade’ that turns and accelerates the hot gases coming from the combustor so that they hit the turning blade just right.
They are usually made from an alloy that not only has a high melting temperature but also retain strength to very close that temperature. They are then coated with a thermal barrier in the form of a ceramic. After that you take air from the compressor which is hot but still cooler and inject it through the vane (cools it) but then make it go out through carefully designed holes on the surface so that the cooler air comes out n a thin layer like a shield over the surface creating an air curtain that further shields it.
It is probably one of the most engineered portions of the engine and designed so that it can take the hottest combustion air coming from the combustor. That air is not uniformly hot but has some spots that tend to not move much and are really hot.
The rotating turbine blade on the other hand is moving through that hot spot but also through the coolest spot so it sees more of an average. It does however have to stay together while being pulled hard so it also needs cooling but the thermal input is lower than for the static vanes. Also as you move down the cascade of turbines extracting power from the gases they cool down and life gets easier.
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