It is known that some Grothendieck rings of categories of representations of quantum affine algebras can be endowed with cluster algebras structures. This is true for example for certain categories O containing the category of finite-dimensional representations. On the other hand, certain Grothendieck rings of categories of finite dimensional representations admit remarkable t-deformations, which are linked to quiver varieties and are useful to compute characters. The aim of this work is to obtain such t-deformations in the context of categories O. Our approach is based on quantum cluster algebras.