This work investigates multi-resolution methodologies for simulating dimer models. The solvent particles which make up the heat bath interact with the monomers of the dimer either through direct collisions (shortrange) or through harmonic springs (long-range). Two types of multi-resolution methodologies are considered in detail: (a) describing parts of the solvent far away from the dimer by a coarser approach; (b) describing each monomer of the dimer by using a model with different level of resolution. These methodologies are then utilised to investigate the effect of a shared heat bath versus two uncoupled heat baths, one for each monomer. Furthermore the validity of the multi-resolution methods is discussed by comparison to dynamics of macroscopic Langevin equations.