Lattice and core physics modeling and calculations have been performed to quantify the impact of power/flux levels and power history on the reactivity and achievable burnup for 35-element fuel bundles made with thorium-based fuels, such as (Pu,Th)O2 and (233U,Th)O2. These bundles are designed to produce on the order of 20 MWd/kg burnup in homogeneous cores in a 700-MW(electric)–class pressure-tube heavy water reactor, operating on a once-through thorium cycle. Methods have been developed to model time-dependent power histories in lattice physics calculations that are more consistent with core physics analysis results. Results demonstrate that the impact of power/flux level and the modeling of time-dependent power histories on the core power distributions and achievable fuel burnup are modest for Pu/Th fuels but are more significant for 233U/Th fuels. Thus, to reduce the neutron capture rate in 233Pa and to increase fuel burnup and fissile utilization, there may be an incentive to develop solutions to reduce the time-average specific power in the fuel.