Hello everyone!
My computer has 4-core processor. However, when I play with The Many Faces Of Go, it uses only one core.
How can I tune it to use more? Would be great to have a faster/stronger opponent.

Can't be done without rewriting the program. Programs have to be coded to take advantage of multiple cores. Older software usually cannot do it.

I have just found out that it does use all 4 cores, but only if the highest (2k) strength is chosen.
If I tune it to 4k, it uses only one core. That's why 4k is weaker but not faster.

Maybe you need to be more explicit about what you have there. What version of MFOG and what are you running it on. Your references to 2k and 4k lead me to believe that you have only an early version of MFOG 12, because that's what it was when first released 10/31/2008.

After which came a long sequence of fix updates. It wasn't till the 11/6/2010 update that MFOG became 1d and 3k for the top levels (only the two top levels of MFOG 12 uses MCTS). The latest update I see is for 1/23/2011. Since those updates are free to anybody who owns MFOG, not fair to describe MFOG 12 only in its original incarnation, bugs and all.

BTW, the weakening of MCTS programs is tricky business. You can't (or at least shouldn't) assume that the developer has done it simply by reducing the number of playouts and thus having it run faster. While that method would weaken the program, it might result in very erratic play. There are a lot of alternatives to make a MCTS play weaker while retaining reasonable play. Let me give an example (one I know Fotland did NOT use). Suppose we assign a probability 0<p<1 that we use the second best move instead of the best (according to MCTS) and at each move generate a (pseudo)random number in the range of 0-1. If this number is less than p, make the second best move, otherwise the best. Then the value of "p" can act a slider to select playing strengths between always using the best move and always using the second best. This method would NOT play at a different speed.