This paper develops an FMI-oriented one-dimensional transient thermal-hydraulic model for separated heat pipes used in passive residual heat-removal systems. The heat pipe is represented by modular control volumes for the evaporator, vapor riser, condenser, downcomer, wick, wall, vapor chamber, and external water tank. The model combines a nodal thermal-resistance network with a Knudsen-number startup criterion, vapor pressure-drop closure, Clausius-Clapeyron temperature-pressure coupling, phase-change source terms, and capillary/gravity-assisted return-flow closure. The resulting ordinary differential equations are solved using a three-stage Gauss-Legendre implicit Runge-Kutta method. To address system-level reuse, the physics, solver, parameters, inputs, outputs, and state-update routines are organized according to FMI Co-Simulation semantics, enabling later FMU wrapping without changing the core solver. Validation against small-scale and large-scale heat-pipe data shows temperature and flow-rate deviations of approximately 10% or less, supporting fast integration in Modelica-based accident-transient simulations.