We study the linear evolution of a Gaussian pulse injected at different locations along a one-dimensional (1D), hot (T ≥ 6.3 MK) coronal loop, including the dissipative effects of thermal conduction, viscosity, heating, and radiative cooling. We consider both homogeneous and stratified loops of different lengths (50 ≤ L ≤ 400 Mm) and values of the pulse width (or standard deviation, βg/L) between 0.005 and 0.02. We find that a Gaussian velocity pulse can generate propagating waves whose amplitudes increase with increasing width of the pulse. The shape of the waves is quite irregular owing to the superposition of the several harmonics composing the Gaussian pulse. Wave damping due to the combined effects of thermal conduction and viscosity is faster in the shortest and hottest loops. The decay times and periods of the waves are within the observed values of decaying modes of hot SUMER loop oscillations.