  Thanks to modern manufacturing technologies, heterogeneous materials with
complex inner structures (e.g., foams) can be easily produced. However, their
utilization is not straightforward, as the classical constitutive laws are not
necessarily valid. According to various experimental observations, the
Guyer--Krumhansl equation stands as a promising candidate to model such complex
structures. However, the practical applications need a reliable and efficient
algorithm that is capable of handling both complex geometries and advanced heat
equations. In the present paper, we present the development of a $hp$-type
finite element technique, which can be reliably applied. We investigate its
convergence properties for various situations, being challenging in relation to
stability and the treatment of fast propagation speeds. That algorithm is also
proved to be outstandingly efficient, providing solutions four magnitudes
faster than commercial algorithms.
