Isogeometric analysis is an evolution of the finite element method: it employs B-splines or their generalization both to represent the computational domain and to approximate the solution of the considered partial differential equation. The high-continuity of isogeometric basis functions leads to several advantages, e.g. higher accuracy per degree-of-freedom, but it introduces also challenging problems at the computational level: one of the major issues is the efficient solution of linear systems. In this talk, I will focus on the study of an efficient solver for a Galerkin space-time isogeometric discretization of the heat equation. Exploiting the tensor product structure of the basis functions in the parametric domain, I propose a preconditioner that can be efficiently applied thanks to an extension of the classical Fast Diagonalization method. The preconditioner is robust w.r.t. polynomial degree and the time required for the application is almost proportional to the number of degrees-of-freedom. This is based on a joint work with G. Sangalli, M. Tani and G. Loli.