<p>This paper presents the novel Isogeometric Finite Volume Method (IGFVM) for the numerical solution of steady-state heat transfer problems. The method utilizes the finite volume method (FVM) to derive integral balance equations over control volumes and Isogeometric analysis (IGA) to represent the solution field, resulting in an accurate representation of the problem’s geometry. The proposed approach is based on a dual mesh representation: the first mesh is used for the geometry and solution field, and the second mesh is used for the control volume discretization. NURBS-based representations are employed for the geometry and solution mesh. The control volume mesh is generated based on the geometry mesh, enabling the balance equations to be applied precisely on control volumes that exactly replicate the geometry. This eliminates inconsistencies between the problem’s geometry and the analysis model. The results demonstrate the validity of the proposed formulation and its capability to bridge the gap between accurate geometric representations of complex domains and numerical analysis. Furthermore, the use of NURBS enables easy incorporation of higher polynomial degrees, supporting solution fields with high continuity. Numerical studies on one and two-dimensional problems are presented, along with a comparison to the well-established Galerkin Isogeometric Analysis (IGA). A representative MATLAB implementation is provided as supplementary material. The results demonstrate the validity of the proposed formulation and its capability to bridge the gap between accurate geometric representations of complex domains and numerical analysis.</p>