The design of a thermal regenerator is initially carried out by considering the fundamental influencing variables. For novel solid-state cooling systems using active caloric regenerators, the non-linearity of the coupled phenomena of material properties, heat transfer, and hydraulic flow can complicate the interpre- tation of experimental and simulated results. Based on the boundary conditions of a sinusoidal magnetic field and fluid flow, we elucidate the operation of active regenerators by deriving easy-to-manage analyt- ical expressions for the temperature transients of the caloric materials and heat transfer fluid. An internal temperature measurement system with an estimated uncertainty of ±0.3 K for packed bed regenerators has been developed for validation. The derived expressions have acceptable accuracy relative to the exper- imental and numerical results for temperature profiles in both magnitude and sensitivity, where average and maximum errors are ∼10% and ∼15%, respectively. Useful figures of merit are post-calculated using the derived temperature profiles. We found that the average temperature profiles are linear for passive regenerators and nonlinear for active regenerators, and their transients are nonlinear functions of the configuration and operating parameters.