With the growing importance of regenerative power generation and especially of a hydrogen-based economy, the full potential of gas turbines of the smaller output class (<10 MW) can be ideally exploited to provide peak coverage of the energy need whilst stabilizing the electric grids in the mid- and low-voltage range. Such machines can be typically started in a relatively short time (similarly to aero engines) and are capable, at the same time, of delivering dispatchable power-on-demand. A safe, stable and profitable operation under highly unsteady conditions poses renewed challenges for an optimal thermal management (especially in the HP stages) as well as control and surveillance of the machines. The understanding and hence predictability of the propagation of the temperature inhomogeneities originating at the combustor outlet remains hence a primary objective of current research, as persistent distortion patterns could be adopted at the turbine exhaust as diagnostic indications of a malfunction of the combustor, for example. In the present study, low-frequency disturbances introduced by a periodic load variation have been simulated and superimposed to the inhomogeneous, unsteady flow entering a three-stage, high-pressure industrial gas turbine fed by a can-type combustion chamber comprising six silo-burners. The effects of the unsteadiness realized at the combustor exit have been investigated by means of Detached Eddy Simulations, whereby a density-based solution approach with detailed thermodynamics has been employed. The periodic disturbances at the turbine inlet have been obtained by means of an artificially generated, unsteady field, resulting from a two-dimensional snapshot of the flow field at the combustor exit. Also, a combustor failure has been mimicked by reducing (respectively increasing) the mean temperature in some of the turbine inlet regions corresponding to the outlet of two burners. The propagation and amplitude changes of temperature fluctuations have been analyzed in the frequency domain. Tracking of the temperature fluctuations' maxima at the lowest frequencies revealed characteristic migration patterns indicating that the corresponding fluctuations persist with a non-negligible amplitude up to the last rows. A distinct footprint could also be observed at the same locations when a combustor failure was simulated, showing that, in principle, the early detection of combustor failures is indeed possible.