The collision energy dependence of the fragmentation of the 1-bromonaphthalene radical cation was studied using sustained off-resonance excitation (SORI) in a 7 T Fourier transform ion cyclotron resonance mass spectrometer (FTMS). Fragmentation efficiency curves were obtained as a function of collision energy at four different pressures of Ar bath gas corresponding to collision numbers of 3, 5, 15, and 20. The results were modeled using RRKM/QET formalism. A refined analytical form for the collisional energy deposition function is proposed. The ability to obtain accurate fragmentation energetics of a complex system using the present approach is demonstrated. The "effective temperatures" deduced from the average internal energies for C6H5Br+. and C10H7Br+. were found to be the same for both ions provided the bath gas pressure and the maximum value of center-of-mass collision energy were the same. The range of effective temperatures from 1000 to 3700 K sampled in the present study significantly exceeds the temperature range accessible by blackbody infrared radiative dissociation (BIRD). We anticipate that the present approach can be used to study fragmentation energetics of biomolecules.