Aims.Using a newly developed algorithm, we map, to the highest angular resolution allowed by the data, the temperature structure of the intra-cluster medium (ICM) within a nearly complete X-ray flux limited sample of galaxy clusters in the redshift range between ${z}=0.045$ and ${z}=0.096$. Our sample contains seven bright clusters of galaxies observed with XMM-Newton: Abell 399, Abell 401, Abell 478, Abell 1795, Abell 2029, Abell 2065, Abell 2256. Methods.We use a multi-scale spectral mapping algorithm especially designed to map spectroscopic observables from X-ray extended emission of the ICM. By means of a wavelet analysis, this algorithm couples spatially resolved spectroscopy with a structure detection approach. Deriv...