A three-dimensional whole-core transient coupled thermal-hydraulic and neutronics code system for modeling prismatic high-temperature gas-cooled reactors (HTGRs) is presented. The discrete ordinates method code PHANTOM-SN was used to solve the multigroup neutron transport problem with cross sections generated with Serpent. The new finite element code OPERA was developed to solve the heat equation in the core and includes simplified subcodes for the coolant, reactor pressure vessel, and concrete containment building, as well as the power conversion cycle. Core graphite thermal conductivity degradation is included as a function of temperature and irradiation temperature. A 20-MW(thermal) HTGR design was modeled using the coupled multiphysics code to prove inherent safety. We simulated steady state, a depressurized loss of forced cooling (DLOFC), a partial blockage, and a reactivity insertion incident. We show that the DLOFC is not the most severe scenario for the fuel temperature in this prismatic micro HTGR. Upon a DLOFC, the peak fuel temperature remains well below the tri-structural isotropic (TRISO) fuel limits, even when the power is increased to 40 MW(thermal). However, during a partial blockage incident of one fuel assembly stack, the maximum fuel temperature reaches 2300°C, severely exceeding the limits. We furthermore contend that the graphite thermal conductivity values used in modeling should always be made explicit and that the temperature of irradiation should be included as a parameter since it can cause a sharp decrease (up to 97%) in the conductivity. We show that using unirradiated graphite parameters leads to an underestimation in peak temperature of 165°C while using a relatively low power density compared to other HTGRs. Finally, we argue that for prismatic HTGRs with a central reflector, bypass flow may lower the maximum fuel temperature.