  In order to account for non-Fourier heat transport, occurring on short time
and length scales, the often-praised Dual-Phase-Lag (DPL) model was conceived,
introducing a causality relation between the onset of heat flux and the
temperature gradient. The most prominent aspect of the first-order DPL model is
the prediction of wave-like temperature propagation, the detection of which
still remains elusive. Among the challenges to make further progress is the
capability to disentangle the intertwining of the parameters affecting
wave-like behaviour. This work contributes to the quest, providing a
straightforward, easy-to-adopt, analytical mean to inspect the optimal
conditions to observe temperature wave oscillations. The complex-valued
dispersion relation for the temperature scalar field is investigated for the
case of a localised temperature pulse in space, and for the case of a forced
temperature oscillation in time. A modal quality factor is introduced showing
that, for the case of the temperature gradient preceding the heat flux, the
material acts as a bandpass filter for the temperature wave. The bandpass
filter characteristics are accessed in terms of the relevant delay times
entering the DPL model. The optimal region in parameters space is discussed in
a variety of systems, covering nine and twelve decades in space and time-scale
respectively. The here presented approach is of interest for the design of
nanoscale thermal devices operating on ultra-fast and ultra-short time scales,
a scenario here addressed for the case of quantum materials and graphite.
