  We consider certain results for the heat kernel of nonminimal operators. The
general expressions provided by Gusynin and Kornyak resulting from symbolic
computation programmes for n dimensions are evaluated for 4 dimensions which
are checked against results given by Barvinsky and Vilkovisky. We also check
that the results in flat space are consistent with earlier results of
Guendelmen et al. We then consider a powerful construction of the Green
function of a nonminimal operator by Shore for covariantly constantly gauge
fields in flat spacetime, and employ dimensional arguments to produce a check
on the gauge parameter dependence of a certain coefficient. The connection of
the results for heat kernel coefficients emanating from the construction of
Shore, to those from other techniques is hereby established for the first time.
