  In the presented paper we tackle the problem of the effective field theory in
curved spacetime (cEFT) construction. To this end, we propose to use the heat
kernel method. After introducing the general formalism based on the well
established formulas known from the application of the heat kernel method to
deriving the one-loop effective action in curved spacetime, we tested it on
selected problems. The discussed examples were chosen to serve as a check of
validity of the derived formulas by comparing the obtained results to the known
flat spacetime calculations. On the other hand, they allowed us to obtain new
results concerning the influence of the gravity induced operators on the
effective field theory without unnecessary calculational complications.
