  We present an implementation of a fully self-consistent finite temperature
second order Green's function perturbation theory (GF2) within the diagrammatic
Monte Carlo framework. In contrast to the previous implementations of
stochastic GF2 ({\it J. Chem. Phys.},{\bf 151}, 044144 (2019)), the current
self-consistent stochastic GF2 does not introduce a systematic bias of the
resulting electronic energies. Instead, the introduced implementation accounts
for the stochastic errors appearing during the solution of the Dyson equation.
We present an extensive discussion of the error handling necessary in a
self-consistent procedure resulting in dressed Green's function lines. We test
our method on a series of simple molecular examples.
