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A relationship between Feynman-Kac formula and parametrix representation for Schroedinger semigroup proves to be useful for evaluation of the regularized trace and calculation of the heat invariants. In view of the asymptotic analysis carried out for evolutionary semigroups beyond the diffusion type class we revisit path integral approach to the study of heat kernel asymptotics and heat trace estimations. Within this approach for the case of diffusion with a drift the heat kernel asymptotic properties are specified. Making use of parametrix expansion and Born approximation we investigate semigroups generated by potential perturbations of biLaplacian.