We present a protocol for actively suppressing Gauss law violations in quantum simulations of SU(2) lattice gauge theory. Mid-circuit measurements extract a syndrome $(J,M,N)$ characterizing the gauge-violation sector at each vertex by resolving both the total angular momentum and the magnetic quantum numbers of the violation through a group quantum Fourier transform. A syndrome-conditional recovery operation maps the state back to the gauge-invariant subspace, and the procedure is iterated as a sweep over vertices in a process we call gauge cooling. We prove that every single-qubit Pauli error at a coordination-four vertex with four spin-$1/2$ edges is detected by the gauge syndrome, and we show that the Knill–Laflamme conditions fail for syndrome-based recovery alone whenever the singlet multiplicity exceeds one. The residual physical-subspace errors carry a structured Pauli decomposition occupying only three of the four Pauli directions, a strongly biased channel suited to concatenation with a bias-tailored stabilizer code. We demonstrate the protocol on a single-plaquette simulation of the Kogut–Susskind Hamiltonian truncated to the spin-$1/2$ representation under depolarizing and amplitude damping noise, and we observe that gauge cooling restores approximate gauge invariance and improves fidelity at noise rates representative of current superconducting hardware. The improvement is in unconditional fidelity; post-selection on the physical subspace remains the more accurate of the two at this system size, so gauge cooling is best understood as trading logical fidelity for the removal of a post-selection overhead that grows with lattice size. We further find that the protocol requires the syndrome readout to be repeated, since a single misread syndrome among the roughly one thousand conditional recoveries of a run is enough to negate the advantage.