In our former study (J. Phys. A: Math. Theor. 43, (2010) 325210) we introduced a modified
Fourier-Cattaneo law and derived a nonautonomous telegraph-type heat conduction equation
which has desirable self-similar solution. Now we present a detailed in-depth analysis
of this model and discuss additional analytic solutions for different parameters.
The solutions have a very rich and interesting mathematical structure due to various