  We consider functions of multi-dimensional versions of truncated Wiener--Hopf
operators with smooth symbols, and study the scaling asymptotics of their
traces. The obtained results extend the asymptotic formulas obtained by H.
Widom in the 1980's to non-smooth functions, and non-smooth truncation domains.
The obtained asymptotic formulas are used to analyse the scaling limit of the
spatially bipartite entanglement entropy of thermal equilibrium states of
non-interacting fermions at positive temperature.
