Simulation of the low-temperature properties of many-body systems remains one of the major challenges in theoretical and experimental quantum information science. We present, and demonstrate experimentally, a universal (pseudo) cooling method that is applicable to any physical system that can be simulated by a quantum computer. This method allows us to distil and eliminate hot components of quantum states like a quantum Maxwell's demon. The experimental implementation is realized with a quantum optical network, and the results are in full agreement with theoretical predictions (with fidelity higher than 0.978). Applications of the proposed pseudo-cooling method include simulations of the low-temperature properties of physical and chemical s...