  Among the numerous heat conduction models, the Guyer--Krumhansl equation has
a special role. Besides its various application possibilities in
nanotechnology, cryotechnology, and even in case of modeling heterogeneous
materials, it poses additional mathematical challenges compared to the Fourier
or Cattaneo {(a.k.a. Maxwell--Cattaneo--Vernotte)} equations. Furthermore, the
Guyer--Krumhansl equation is the first heat conduction model, which includes
the curl of the heat flux density in the evolution equation. In the present
paper, we place our focus on the consequences of the existence of such whirling
heat current density by solving the two-dimensional Guyer--Krumhansl equation
with a space and time-dependent heat pulse boundary condition. The
discretization poses further challenges in regard to the boundary condition for
which we propose a particular extrapolation method. Furthermore, with the help
of the Helmholtz decomposition, we show the analogy with the linearized
acoustics of Newtonian fluids, which reveals how the heat flux density plays
the role of the velocity field. Our solutions also reveal an unexpected
temperature evolution caused by the whirling heat flux density, namely, the
temperature can locally be decreased for a short time in a case when the curl
of the heat flux density dominates the heat conduction process.
