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In this paper, we show that it is possible to significantly boost the heat extraction ability of the ICO fridge by applying N identical thermalising channels in a superposition of N cyclic causal orders[2], and that this can be further boosted in the ultracold regime by replacing the working qubit with a quDit working substance. Moreover, we show that for the alternative controlled-SWAPs scheme presented in [1] where one additionally has access to the reservoir qubits which are quantum correlated with the control-target system, the performance can be greatly enhanced in general (tripled for all N and temperatures). Then inspired by [3, 4], we show that quantum coherent control between thermalising a working system with one of N identical thermalising channels (where causal indefiniteness plays no role) yield same advantages in controlled-SWAPs scheme compared to the generalised N-SWITCH protocol for the thermodynamic task described in [1]. We also provide an experimental simulatable quantum cooling protocol with coherently-controlled thermalising channels and notice that it can outperform ICO refrigerator with some specific implementations of the thermalising channel in the case when we only have access to the control-target system. These 2 quantum cooling protocols bear much lower circuit complexity compared to the one with indefinite causal order which makes it more accessible for implementation of this type of nonclassical refrigerator with cutting edge quantum technologies.