My understanding is that the requirement to turn on cowl (inlet lip) anti-ice, which also raises the idle setting, at temperatures above 0C TAT has more to do with the indicated TAT range at which you can have supercooled water droplets due to atmospheric convective or precipitation action and the difference between OAT and TAT rather than any temperature drop the air experiences passing through the inlet. As said above, in high speed flight and in low speed low power flight the air temperature rises slightly as it slows down in the inlet.