Fault-tolerant quantum processors will require continuous millikelvin cooling for far more qubits, control lines and readout chains than today’s systems. Nearly all such cooling relies on ³He/⁴He dilution refrigeration, and the supply of ³He is limited and does not scale with the number of installed systems. Continuous adiabatic demagnetization refrigeration (cADR) offers a path towards a scalable cryogenic infrastructure at millikelvin temperatures that is independent of ³He and other scarce materials. We will review the physics of magnetocaloric cooling and the three factors that limit cADR cooling power below 50 mK: the entropy available in the refrigerant, the thermal boundary conductance between refrigerant and copper, and the thermal conductance of the heat switches. We use a coupled thermal model, validated against measurements, to reproduce the system’s cooling behavior and to guide component design for continuous operation at 20 mK. We will present first performance data and outline the path to a modular cryogenic architecture based on magnetic refrigeration.