An analytical solution for the temperature and heat flux distribution in the case of a semi-infinite solid of constant properties is investigated. The solutions are presented for time-dependent, surface hear fluxes of the forms : (i) Q(1) (t) = Q(0)(1 + a cos omega t); and (ii) Q(2)(t) = Q(0)(1 + bt cos omega t), where a and b are controlling factors of the periodic oscillations about the constant surface heat flux Q(0). The dimensionless (or reduced) temperature and heat Aux solutions are presented in terms of decompositions C-Gamma and S-Gamma of the generalized representation of the incomplete Gamma function. It is demonstrated that the present analysis covers the limiting case for large times which is discussed in several textbooks, for the case of steady periodic-type surface heat fluxes. in addition, an illustrative example problem on heating of malignant tissues, making use of transient and long-time solutions, is also presented.