We present a method for the calculation of the a(3/2) heat kernel coefficie
nt of the heat operator trace for a partial differential operator of Laplac
e type on a compact Riemannian manifold with oblique boundary conditions. U
sing special case evaluations, restrictions are put on the general form of
the coefficients, which, supplemented by conformal transformation technique
s, allows the entire smeared coefficient to be determined.