  We outline a proposal, based on the Heat-Kernel method, to compute 1PI
effective action up to any loop order for quantum field theory with scalar and
fermion fields. We algebraically extract the divergences associated with the
composite operators without explicitly performing any momentum loop integral.
We perform this analysis explicitly for one and two-loop cases and pave the way
for three-loop as well. Using our prescription we compute the two-loop counter
terms for a theory containing higher mass dimensional effective operators that
are polynomial in fields for two different cases: (i) real singlet scalar, and
(ii) complex fermion-scalar interacting theories. We also discuss how the
minimal Heat-Kernel fails to deal with the effective operators involving
derivatives. We explicitly compute the one-loop counter terms for such a case
within an $O(n)$ symmetric scalar theory employing a non-minimal Heat-Kernel.
Our method computes the counter terms of the composite operators directly and
is also useful for extracting infrared divergence in massless limits.
