In this paper, we analyzed non-stationary fluctuations of heat flux and inlet pressure recorded during the boiling of water in a new model of a heat exchanger containing 11 parallel mini-channels covered with a steel mesh coated with AlN, CrN, and SiO2. The use of the steel mesh increases the average heat flux absorbed by the exchanger and modifies two-phase flow patterns in mini-channels. The recorded parameters during the experiment are chaotic due to the complex thermal and hydraulic interactions between processes occurring inside the neighboring channels. Additionally, rapid phase changes occur in small volumes within the channels, leading to rapid nucleation processes that push the liquid in both inlet and outlet directions, causing so-called ‘reverse flows,’ which block two-phase flow in the mini-channels. As a result, an attractor reconstructed from heat flux and pressure changes consists of a ‘kernel’ containing the system’s trajectories formed by two-phase flow patterns in channels and ‘attractor spikes’ corresponding to the reverse flows. The relationship between the attractor’s spikes and its core was analysed based on correlation between the changes of entropy of microstates (two-dimensional matrices of points) on recurrence and non-recurrence plots. The obtained results show that the highest heat flux was observed in the case of the weakest negative correlation between analysed entropies, in the case of CrN mesh coating. This indicates CrN mesh enabled flow stabilization by mitigating the reverse flows effect in the mini-channels (lower inlet pressure, higher outlet water temperature).