This paper presents the analysis of classical heat conduction solutions applied to materials characterization. The formulas for parametric derivatives are obtained and illustrated to demonstrate the evolution of the relative sensitivity functions in time. The potential of using both front-surface and rear-surface solutions for determining material thermal properties, sample thickness, and surface heat exchange parameters is discussed. The roots of the well-known transcendent equation for a non-adiabatic plate are approximated in a polynominal form. Some practical applications of the proposed formulas are reported.