Triplet-excited-state energies of perylene-monoimides (PMIs) lie in the range 1.12 eV +/- 2 meV when compared to singlet-excited-state energies of about 2.39 eV +/- 2 meV; therefore, the corresponding naphthalene-linked PMI-Dimer was investigated as a novel singlet-fission (SF) material. Ultrafast transient absorption measurements demonstrated the (S1S0)-to-(1)(T1T1) transformation and the involvement of a mediating step in the overall (1)(T1T1) formation. The intermediate is a charge-transfer state that links the initial (S1S0) with the final (1)(T1T1), and imposes charge-transfer character on both, which are thus denoted (S1S0) CT and (1)(T1T1)(CT). At room temperature, the decorrelation and stability of (1)(T1T1)(CT) is affected by the geminate triplet-triplet recombination (G-TTR) of the two triplets. Independent confirmation for G-TTR to afford upconverted (S1S0)(UC) in fsTA and nsTA measurements with PMI-Dimer, came from probing PMI-Monomer (T-1)s in triplet-triplet annihilation up-conversion (TTA-UC). The G-TTR channel, active in the PMI-Dimer at room temperature, is suppressed by working at either low temperatures (similar to 140 K) or in polar solvents (benzonitrile): Both scenarios assist in stabilizing (T1T1)(CT). As a consequence, the triplet quantum yields are 4.2% and 14.9% at room temperature and 140 K, respectively, in 2-methyltetrahydrofuran.