The quantum Grothendieck rings of certain categories of representations of quantum affine algebras admit remarkable t-deformations called quantum Grothendieck rings. This notion was first introduced, via the study of quiver varieties, for categories of finite-dimensional representations, when the underlying Lie algebra is of simply laced type. This construction was then algebraically generalized to non simply laced types. In this talk, we will focus on a category O^+ of representations, and we will see how the quantum Grothendieck ring of this category can be define combinatorally, as a quantum cluster algebra. In particular, we will discuss this construction in non simply laced types.