For linear Fourierian, quasi-one-dimensional heat conduction in a stack of homogeneous layers, it is shown that the temperature decay constants, τn, behave asymptotically as n−2. This yields a considerable lowering of computer time at a satisfactory accuracy level. A numerical example is given. The matching problem of the alternative infinite series containing terms such ase−t/τ ande−a/t, respectively, is also considered, and the equivalence between surface excitation and a volume excitation is demonstrated.