For a complex manifold X the ring of microdifferential operators \mathcal{E}_X acts on the microlocalization \mu hom(F,\mathcal{O}_X) for F in the derived category of sheaves on X . Kashiwara, Schapira, Ivorra, Waschkies proved as a byproduct of their new microlocalization functor for ind-sheaves, \mu_X , that \mu hom(F,\mathcal{O}_X) can in fact be defined as an object of \mathrm{D}(\mathcal{E}_X) : this follows from the fact that \mu_X \mathcal{O}_X is concentrated in one degree.In this paper we prove that the tempered microlocalization T - \mu hom(F,\mathcal{O}_X) and in fact \mu_X \mathcal{O}_X^t also are objects of \mathrm{D}(\mathcal{E}_X) . Since we don't know whether \mu_X \mathcal{O}_X^t is concentrated in one degree we built resolutions of \mathcal{E}_X and \mu_X \mathcal{O}_X^t such that the action of \mathcal{E}_X is realized in the category of complexes (and not only up to homotopy). To define these resolutions we introduce a version of the de Rham algebra on the subanalytic site which is quasi-injective. We prove that some standard operations in the derived category of sheaves can be lifted to the (non-derived) category of dg-modules over this de Rham algebra. Then we built the microlocalization in this framework.