Quantum circuits interact with the environment via several temperature-dependent degrees of freedom. Multiple experiments to-date have shown that most properties of superconducting devices appear to plateau out at T ≈ 50 mK – far above the refrigerator base temperature. This is for example reflected in the thermal state population of qubits, in excess numbers of quasiparticles, and polarisation of surface spins – factors contributing to reduced coherence. We demonstrate how to remove this thermal constraint by operating a circuit immersed in liquid3He. This allows to efficiently cool the decohering environment of a superconducting resonator, and we see a continuous change in measured physical quantities down to previously unexplored sub-mK temperatures. The3He acts as a heat sink which increases the energy relaxation rate of the quantum bath coupled to the circuit a thousand times, yet the suppressed bath does not introduce additional circuit losses or noise. Such quantum bath suppression can reduce decoherence in quantum circuits and opens a route for both thermal and coherence management in quantum processors.