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Plot the results with different values of that parameter in the same figure and see if they converge. Kappa should not be sensitive to that parameter if it is chosen in an appropriate range. I think theoretically, the larger the time constant (with weaker coupling to thermostat) , the better the results. But the simulation time needed to achieve steady state (with well-defined temperature gradient) may also increase with increasing time constant, making the computation more time consuming. Good luck to you!
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