I'm not sure what you're asking. I presume LAMMPS itself
is doing the right thing on 1 or 4 or 8 procs, i.e. the output
thermodynamics is correct. Note that 2 runs can
be different due to round-off or different inititialization in
parallel, yet still both be statistically correct.
Then you are measuring heat flux by some means (you don't say
how), but I presume it is just a diagnostic, and getting different
answers. If it is your method for doing this, then you will need
to debug your 2 answers and figure out what is making them
different.
Steve