  The issue related to the so-called dimensional reduction procedure is
revisited within the Euclidean formalism. First, it is shown that for symmetric
spaces, the local exact heat-kernel density is equal to the reduced one, once
the harmonic sum has been succesfully performed. In the general case, due to
the impossibility to deal with exact results, the short time heat-kernel
asymptotics is considered. It is found that the exact heat-kernel and the
dimensionally reduced one coincide up to two non trivial leading contributions
in the short time expansion. Implications of these results with regard to
dimensional-reduction anomaly are discussed.
