A new approach to obtain a volumetric discretization from a T-spline surface representation is presented. A T-spline boundary zone is created beneath the surface, while the core of the model is discretized with Lagrangian elements. T-spline enriched elements are used as an interface between isogeometric and Lagrangian finite elements. The thickness of the T-spline zone and thereby the isogeometric volume fraction can be chosen arbitrarily large such that pure Lagrangian and pure isogeometric discretizations are included. The presented approach combines the advantages of isogeometric elements (accuracy and smoothness) and classical finite elements (simplicity and efficiency). Different heat transfer problems are solved with the finite element method using the presented discretization approach with different isogeometric volume fractions. For suitable applications, the approach leads to a substantial accuracy gain.