Repeated transient simulations of Brayton cycles are often required during parameter studies, control assessment, and design iteration, whereas direct Modelica simulation under many conditions can remain inefficient despite its flexibility for system-level dynamic modeling. A parametric reduced-order modeling method is developed for fast transient prediction of Modelica-based Brayton cycles under unseen parameters and new operating conditions. Transient data from a Modelica model of a Helium-Xenon Brayton cycle are used to construct a baseline-regularized Dynamic Mode Decomposition with control reduced-order model, in which state trajectories are formulated as deviations from local steady baselines and measured auxiliary inputs are incorporated through the control channel. A Secondary Dynamic Mode Decomposition strategy is further introduced to generalize reduced-order quantities along the parameter direction. Results show accurate interpolation and stable extrapolative prediction against Modelica reference simulations, supporting rapid transient evaluation of Brayton cycles and offering a new perspective for broader fast transient prediction.