The diffusion of dopant atoms to the surface of a refractory cathode doped with a lowering work-function dopant is considered. The variations of the cathode temperature with time and with the coordinate along the cathode length are taken into account. It is shown that, depending on the value of , the work function at the monolayer coverage, there are two possible scenarios of cathode temperature development. At low , the cathode experiences instability which leads to cleaning of the surface from adatoms and to a sharp rise in temperature. At higher , the cathode temperature changes gradually. The cathode service time, as a period of time when the dopant surface concentration falls and the cathode temperature raises, is estimated. It is shown that a properly organized temperature distribution inside the cathode may increase its service life several times.