Numerical methods applied to industrial problems have made great progress, so that today it is possible to reliably model different physical phenomena. A few decades ago, Hughes et al. [1] introduced IsoGeometric Analysis, an "extension" of Finite Element Method, to represent both the geometry and the solution field. In most cases, this method obtains better results by increasing the polynomial degree p or by refining the mesh size h. However, its application implies a great challenge from a computational point of view due to the fact that the cost increases rapidly with the degree p [2, 3, 4]. This communication focuses on novel techniques like "weighted quadrature" [3], "matrix free" [4] and "fast diagonalization" [5] approaches which, coupled with IsoGeometric Analysis, enable to: - Take advantage of the tensor structure of the basis functions, - Reduce storage memory by using much fewer quadrature points, - Improve computation time of matrix-vector products, - Enhance the convergence rate of the iterative solver by introducing an inexpensive, easy to code and effective preconditioner. The objective of this communication is to illustrate the synergy between these different approaches, applied to nonlinear transient heat transfer problems, to allow significant cost reductions. [1] A. Cottrell, T. Hughes, Y. Brazilevs, IGA: Toward Integration of CAD and FEA, Wiley, 2009. [2] P. Antolin, A. Buffa, F. Calabro, M. Martinelli, G. Sangalli, Efficient matrix computation for tensor-product isogeometric analysis: The use of sum factorization, Computer Methods in Applied Mechanics and Engineering 285 (2015) 817–828. [3] F. Calabro, G. Sangalli, M. Tani, Fast formation of isogeometric Galerkin matrices by weighted quadrature, Computer Methods in Applied Mechanics and Engineering 316 (2017) 606–622. [4] G. Sangalli, M. Tani, Matrix-free weighted quadrature for a computationally efficient isogeometric k-method, Computer Methods in Applied Mechanics and Engineering 338 (2018) 117–133. [5] G. Sangalli, M. Tani, Isogeometric preconditioners based on fast solvers for the Sylvester equation, SIAM Journal on Scientific Computing 38 (2016) A3644–A3671.