Adiabatic quantum computation solves problems by finding the ground states of many-body Hamiltonians, but its analysis is challenging. This study proposes an alternative cooling-based method, inspired by cavity cooling, where the system's entropy is extracted by discarding ancilla qubits, driving the system toward its ground state. This cooling approach is computationally equivalent to quantum circuits. We demonstrate its application to combinatorial optimization problems by numerical simulation, incorporating a mechanism that allows the system to escape local energy minima via high-order transitions.