  We study the asymptotics of the heat trace $\Tr\{fPe^{-tP^2}\}$ where $P$ is
an operator of Dirac type, where $f$ is an auxiliary smooth smearing function
which is used to localize the problem, and where we impose spectral boundary
conditions. Using functorial techniques and special case calculations, the
boundary part of the leading coefficients in the asymptotic expansion is found.
