  Estimating the temperature field of a building envelope could be a
time-consuming task. The use of a reduced-order method is then proposed: the
Proper Generalized Decomposition method. The solution of the transient heat
equation is then re-written as a function of its parameters: the boundary
conditions, the initial condition, etc. To avoid a tremendous number of
parameters, the initial condition is parameterized. This is usually done by
using the Proper Orthogonal Decomposition method to provide an optimal basis.
Building this basis requires data and a learning strategy. As an alternative,
the use of orthogonal polynomials (Chebyshev, Legendre) is here proposed.
