Propagation of thermal waves due to localised heat inputs is analysed
by the Laplace transforms method for the case of constant thermophysical
parameters of the heat-conducting media and a temperature dependent
internal heat source. Both the hyperbolic and parabolic models of heat
conduction are used and compared. For the hyperbolic model, an energy
pulse travelling along the conductor is observed. Long time hyperbolic
solutions do not differ qualitatively from the related parabolic
solutions, but the quantitative differences between the two solutions
do not vanish with time because of the temperature dependent heat
source. The cases considered in the paper describe the evolution of
normal zones in technical superconductors.