  The detection of excess of soft X-ray or Extreme Ultraviolet (EUV) radiation,
above the thermal contribution from the hot intracluster medium (ICM), has been
a controversial subject ever since the initial discovery of this phenomenon. We
use a large--scale hydrodynamical simulation of a concordance $\Lambda$CDM
model, to investigate the possible thermal origin for such an excess in a set
of 20 simulated clusters having temperatures in the range 1--7 keV. Simulated
clusters are analysed by mimicking the observational procedure applied to
ROSAT--PSPC data, which for the first time showed evidences for the soft X-ray
excess. For cluster--centric distances $0.4< R/R_{\rm vir}< 0.7$ we detect a
significant excess in most of the simulated clusters, whose relative amount
changes from cluster to cluster and, for the same cluster, by changing the
projection direction. In about 30 per cent of the cases, the soft X-ray flux is
measured to be at least 50 per cent larger than predicted by the
one--temperature plasma model. We find that this excess is generated in most
cases within the cluster virialized regions. It is mainly contributed by
low--entropy and high--density gas associated with merging sub--halos, rather
than to diffuse warm gas. Only in a few cases the excess arises from
fore/background groups observed in projection, while no evidence is found for a
significant contribution from gas lying within large--scale filaments. We
compute the distribution of the relative soft excess, as a function of the
cluster--centric distance, and compare it with the observational result by
Bonamente et al. (2003) for the Coma cluster. Similar to observations, we find
that the relative excess increases with the distance from the cluster center,
with no significant excess detected for $R<0.4R_{\rm vir}$. (abridged)
