This finding underscores the significance of considering non-linearity when striving for precise temperature transferability in CG models, which has not yet been thoroughly considered in previous studies. It is noteworthy that a similar non-linear scheme has been successfully applied in previous studies involving temperature-transferable coarse-graining. In future research, it might be imperative to develop a rigorous theoretical framework that can provide insights into the underlying mechanisms of the observed nonlinearity in the temperature dependence of the CG model.