This paper presents a fundamental locally one-dimensional (FLOD) method for 3-D thermal simulation. We first propose a locally one-dimensional (LOD) method for heat transfer equation within general inhomogeneous media. The proposed LOD method is then cast into compact form and formulated into the FLOD method with operator-free right-hand-side (RHS), which leads to computationally efficient update equations. Memory storage requirements and boundary conditions for both FLOD and LOD methods are detailed and compared. Stability analysis by means of analyzing the eigenvalues of amplification matrix substantiates the stability of the FLOD method. Additionally, the potential instability of the Douglas Gunn (DG) alternating-direction-implicit (ADI) method for inhomogeneous media is demonstrated. Numerical experiments justify the gain achieved in the overall efficiency for FLOD over LOD, DG-ADI and explicit methods. Furthermore, the relative maximum error of the FLOD method illustrates good trade-off between accuracy and efficiency.