<p>A model of continuous quantum refrigerator model is proposed. It consists of one qubit as working substance that is continuously coupled to a pair of engineered reservoirs. Each reservoir includes of an auxiliary qubit that is weakly coupled to a Markovian thermal bath through a collisional interactions. The primary task of this work is to examine the non-Markovian behavior of the working system over time. The second objective of the current work is to investigate the influence of the resulting non-Markovianity on the thermodynamic properties of the device. We show that the dynamics of the working system can be adjusted from a Markovian to a non-Markovian regime by acting on the ratio between the coupling constants in the model. Furthermore, the results show that the non-Markovian regime can improve the device’s thermodynamic performance compared to the Markovian regime without increasing the thermodynamic cost of operation.</p>