Half-metallicity and low magnetic damping are perpetually sought for spintronics materials, and full Heusler compounds in this respect provide outstanding properties. However, it is challenging to obtain the well-ordered half-metallic phase in as-deposited full Heusler compound thin films, and theory has struggled to establish a fundamental understanding of the temperature-dependent Gilbert damping in these systems. Here we present a study of the temperature-dependent Gilbert damping of differently ordered as-deposited ${\mathrm{Co}}_{2}\mathrm{FeAl}$ full Heusler compound thin films. The sum of inter- and intraband electron scattering in conjunction with the finite electron lifetime in Bloch states governs the Gilbert damping for the well-ordered phase, in contrast to the damping of partially ordered and disordered phases which is governed by interband electronic scattering alone. These results, especially the ultralow room-temperature intrinsic damping observed for the well-ordered phase, provide fundamental insights into the physical origin of the Gilbert damping in full Heusler compound thin films.