The Mori-Zwanzig theory, in principle, allows to derive an exact equation of motion for chosen coarse-grained degrees of freedom based on the dynamics of an underlying fine-grained reference system. The coarse-grained equation of motion has the form of a generalized Langevin equation, which can be exploited in coarse-grained, particle based, simulations. In practice, approximations have to be employed to derive an equation of motion which is numerically tractable and also to establish a link between the memory kernel to interactions on the fine-grained level. This gives rise to a hierarchy of generalized Langevin equations, which can be sorted in terms of an accuracy-complexity trade-off. When a mapping scheme for the coarse-graining procedure is chosen such that the number of degrees of freedom in the coarse-grained representation remains large, the application of a complex generalized Langevin equation can be computationally more costly than direct simulations of the underlying fine-grained model. Arguably, the computationally most efficient approach, which allows to combine structural representation and the incorporation of memory effects in coarse-grained equilibrium simulations, is the application of an isotropic memory kernel in terms of a generalized Langevin thermostat. Severe approximations have to be made to derive such a model from more accurate formulations. In particular the independence of random forces between coarse-grained beads has to be assumed, which is not justified in many cases. I will present an alternative, novel route for the parametrization of generalized Langevin thermostat models. It will be demonstrated that the effects of cross-correlated forces between coarse-grained beads can be effectively accounted for by relating the isotropic memory kernel in the coarse-grained many-body model with the memory kernel of a single-particle generalized Langevin equation.[1] [1] Viktor Klippenstein and Nico F.A. van der Vegt, J. Chem. Phys. 154, 191102 (2021)