  Quantum circuits interact with the environment via several
temperature-dependent degrees of freedom. Yet, multiple experiments to-date
have shown that most properties of superconducting devices appear to plateau
out at $T\approx 50$ 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 liquid $^3$He. 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. The $^3$He 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.
