In this paper, we present an experimental and theoretical study of the photo-dissociation of free-flying dimer radical cations of pyrene (C₁₆H₁₀)₂⁺. Experimentally, the dimers were produced in the plasma of an electron cyclotron resonance ion source and stored in an electrostatic ion storage ring, the Mini-Ring for times up to 10 ms and the photo-dissociation spectrum was recorded in the 400 to 2000 nm range. Two broad absorption bands were observed at 550 (2.25 eV) and 1560 nm (0.79 eV), respectively. Theoretical simulations of the absorption spectrum as a function of the temperature were performed using the Density Functional based Tight Binding approach within the Extended Configuration Interaction scheme (DFTB-EXCI) to determine the electronic structure. The simulation involved all excited electronic states correlated asymptotically with the five lowest excited states D₁–D₅ of the monomer cation and a Monte Carlo exploration of the electronic ground state potential energy surface. The simulations exhibit three major bands at 1.0, 2.1 and 2.8 eV respectively. They allow assigning the experimental band at 1560 nm to absorption by the charge resonance (CR) excited state correlated with the ground state of the monomer D₀. The band at 550 nm is tentatively attributed to dimer states correlated with excited states D₂–D₄, in the monomer cation. Simulations also show that the CR band broadens and shifts towards longer wavelength with increasing temperature. It results from the dependence on the geometry of the energy gap between the ground state and the lowest excited state. The comparison of the experimental spectrum with theoretical spectra at various temperatures allows us to estimate the temperature of the stored (C₁₆H₁₀)₂⁺ in the 300–400 K range, which is also in line with the expected temperatures of the ions deduced from the analysis of the natural decay curve.