  The estimation of wall thermal properties by \emph{in situ} measurement
enables to increase the reliability of the model predictions for building
energy efficiency. Nevertheless, retrieving the unknown parameters has an
important computational cost. Indeed, several computations of the heat transfer
problem are required to identify these thermal properties. To handle this
drawback, an innovative approach is investigated. The first step is to search
the optimal experiment design among the sequence of observation of several
months. A reduced sequence of observations of three days is identified which
guarantees to estimate the parameter with the maximum accuracy. Moreover, the
inverse problem is only solved for this short sequence. To decrease further the
computational efforts, a reduced order model based on the modal identification
method is employed. This \emph{a posteriori} model reduction method
approximates the solution with a lower degree of freedom. The whole methodology
is illustrated to estimate the thermal diffusivity of an historical building
that has been monitored with temperature sensors for several months. The
computational efforts is cut by five. The estimated parameter improves the
reliability of the predictions of the wall thermal efficiency.
