Induced disorder in graphene enables changes in electrical and thermal transport. It has been shown previously that disorder is very important for electron cooling in graphene through disorder-assisted electron-phonon scattering, particularly via the supercollisions process. Here we study electron-momentum relaxation due to electron-phonon scattering while increasing the degree of disorder. With in-situ scanning thermal microscopy we monitor the temperature rise in the constriction region of a bowtie-shaped graphene device while increasing the disorder by means of feedback-controlled voltage ramps at high-current densities. Analysis of the combined thermal and electrical measurements in the low bias regime shows that the relative change of the momentum scattering rate vs temperature, as measured at room temperature, increases with strong local disorder. By excluding other candidate mechanisms for this phenomenon, including a change of the charge carriers density and activation of optical phonons, we conclude that the increase we observe in the temperature-dependent component of the scattering rate is likely due to new acoustic phonon scattering channels that open up as disorder increases.