I am dealing with a very slowly converging simulation. The reason I realised is a long tail and thus the slow mixing. So as advised in the cosmomc readme file, I increased the temperature of the chains from 1 to 2. Now my runs are much faster and one of the runs already converged to the desired R−1 value. Now my question is how to readjust the statistics obtained from this run to get the true statistical values for the parameters in question?

In the readme file it says, GetDist can adjust for the temperature automatically. But I am not sure where or how it does.

Another thing regarding this problem is: I understand increasing the temperature means the T is increased in P(x)

^{1/T}. Now is there any upper limit that one should use when you have to increase T. What I mean, is taking T=2 too much of an increase?

It would be very nice to get some references where T is being increased to do the analysis.