We have performed transport measurements on a multi-layer graphene device fabricated by conventional mechanical exfoliation. By using the zero-field resistance of our graphene device as a self-thermometer, we are able to determine the effective Dirac fermion temperature TDF at various driving currents I while keeping the lattice constant fixed. Interesting, it is found that TDF is proportional to Ia where a ~ 1. According to theoretical and experimental studies, the exponent a is given by 2/(2+p) where the charge-phonon scattering rate 1/τph is proportional to TP. Therefore our results yield p ~ 0, suggesting that there is little Dirac fermion-phonon scattering, a great advantage for applications in nanoelectronics.