  It is shown that the heat kernel operator for the Laplace operator on any
covariantly constant curved background, i.e. in symmetric spaces, may be
presented in form of an averaging over the Lie group of isometries with some
nontrivial measure. Using this representation the heat kernel diagonal, i.e.
the heat kernel in coinciding points is obtained. Related topics concerning the
structure of symmetric spaces and the calculation of the effective action are
discussed.
