In Part I of this paper we have given the foundations of the system th
eoretical treatment of the heat flux based on the Laplace transformati
on method. Moreover, in the cases of the half space, the region bounde
d internally by the sphere and the sphere, the authors have proved cri
teria guaranteeing the existence of the convolutional representations
of the heat flux depending on the known temperature. In this Part II t
he authors have solved: the problem and proved the above criteria for
the region bounded internally by the circular cylinder, and the infini
te circular cylinder. Moreover, harmonic processes have also been disc
ussed for the above cases.