  We pick up a method originally developed by Cheng and Tsai for vacuum
perturbation theory which allows to test the consistency of different sets of
Feynman rules on a purely diagrammatic level, making explicit loop calculations
superfluous. We generalize it to perturbative calculations in thermal field
theory and we show that it can be adapted to check the gauge invariance of
physical quantities calculated in improved perturbation schemes. Specifically,
we extend this diagrammatic technique to a simple resummation scheme in
imaginary time perturbation theory. As an application, we check up to O(g^4) in
general covariant gauge the gauge invariance of the result for the QCD
partition function which was recently obtained in Feynman gauge.
