Real buildings and their components experience dynamic thermal transmi
ssion. It is possible to represent thermal transmission as either a su
perposition of local constitutive convolution equations in a local reg
ion of the solid oi as a directed graph network between connected ther
modynamic regions within the solid. Both the local constitutive convol
ution and directed graph network representations are based on response
factors which can, in principle, be used to estimate the dynamic ther
mal transmission of the building components. The response factors can
also be used to predict the performance of the materials under a range
of design loadings. These response factors for each representation ca
n be estimated directly from time series data of the physical observab
les under general stochastic boundary conditions. Indeed, it can be de
monstrated that each of the representations can accurately characteris
e the thermal performance of building components. The purpose of this
paper is to show that only tile local constitutive equations yield, fo
r all cases considered, the correct values for the physical properties
of the materials under test, whereas the directed graph network repre
sentation does not provide consistent estimates. The local constitutiv
e equations allow the measurement of thermal conductivity and transmis
sion of building components in situ, thus providing a unique insight i
nto the actual thermal performance of constructions in use.