Pick a target and let both machines run from ambient. The TEC is quick and clean — until it flattens against its floor. The cryogen keeps going.
Schematic exponential cool-downs: LN₂ toward its −195.8 °C source floor (reach criterion: within 1 °C of target), thermoelectric toward a −60 °C-class floor (design-dependent; single-stage Peltier platforms commonly specify around −25 °C — check each model’s datasheet). Time axis and constants are teaching constructions — real rates depend on stage design and heat load.