In this paper transient problem created by a line heat sourcethat suddenly starts moving with auniform velocity inside isotropic homogeneous thermoelastic half-spaceare studied using the GN theory of generalized thermoelasicity.The problem is reduced to the solution of three differential equationsby introducing the elastic and the thermoelastic potentials. Using theLaplace and Fourier transforms, the solutions are first obtained in thetransform domain. Applying the inverse transforms, the approximatesolutions, valid in short time range, are then derived. Thedisplacements are calculated at the boundary for short time. Also theapproximate region valid for the solutions is given and two specialcases, (i) the source is motionless and (ii) the uncoupled theory, arestudied. Numerical evaluations are presented for the medium of copper.