A popular method to obtain the 1-D conduction heat transfer of multilayered plane geometries is attributed to Stephenson and Mitalas (1971) and Mitalas (1968). It is applied in different forms known as; CTF (Conduction Transfer Functions) or RT (Response factors). Roughly his idea consists in sampling the temperature at each side of a wall at a certain fixed time step (usually one hour). Between sampling points, due to the lack of information, a linear profile for the evolution of those temperatures is imposed. A triangleshaping function is used to get such a piecewise linear profile. The paper proposes an improvement by extending the idea of a shaping function. Instead of assuming a linear evolution, a specially designed second order (parabolic) evolution is enforced.This paper describes the use of the methodology of transient 1D heat transfer in multi-layered walls with a hold element of 2nd order, and applies it to a specific situation with the most common constructive solutions used in Spain in the energy refurbishment field .The methodology is applied to several constructive refurbished solutions that include insulation as improvement. The results obtained are compared with traditional methods and the greater accuracy of the present method is shown. Finally it shows how the traditional 1 order holder presents worst approximations to reality when the enclosure has more inertia and the insulation is placed at the face where the disturbance is caused.