In this work, we study an autonomous refrigerator composed of three qubits [Phys. Rev. Lett. 105, 130401 (2010)] operating with one of the reservoirs at negative temperatures, which has the purpose of cooling one of the qubits. We find the values of the lowest possible temperature that the qubit of interest reaches when fixing the relevant parameters, and we also study the limit for cooling the qubit arbitrarily close to absolute zero. We thus proceed to a comparative study showing that reservoirs at effective negative temperatures are more powerful than those at positive temperatures for cooling the qubit of interest.