I will discuss a microlocal perspective on Iwahori-Whittaker averaging. When applied to the geometric Langlands program, this can be used to generalize a theorem of Faergeman and Raskin about anti-temperedness. Using an idea of Bezrukavnikov and Morton-Ferguson, it also leads to a proof that Gaitsgory's central sheaves coming from tilting representations become tilting after Whittaker averaging. This extends a result of Arkhipov, Bezrukavnikov, Riche and Rider to cover coefficient fields of small characteristic.