Let me start by saying that this might all be wasted effort since I've heard that Jim Thome wants to stay in Minnesota. But now that Cust was non-tendered would it be a good idea to try and sign Thome? If so, how much should we pay him?
Thome had a great 2010 with the Twins putting up a 283/412/627/437 AVG/OBP/SLG/wOBA line over 108 games. But that was his best season at the plate since 2002, plus he didn't have to keep it up over a full season, so I think it would unreasonable to expect him to repeat that performance next year.
Normally, the rough estimation of true talent level that I have scene used is a 5-3-2 weighting giving the greatest weight to the most recent season, but given that I don't think his 2010 performance is reasonable to expect again I want to knock it down to a 4-3-2 weighting. Thome's wOBAs have been .437, .367, and .370 for his 2010, 2009, and 2008 seasons, respectively. Using the 4-3-2 weighting that gives us a .403 wOBA. That would be good for approximately 5.0 WAR over 162 games in 2010's run environment. However, Thome is 40 years old and has only played in 108 and 124 games over the last two seasons. I would put him at 115 games for 2011 because part of Thome only playing 108 games last year was because of Minnesota's usage choices, not health. That brings us down to 3.6 WAR. Also, I would take off 0.7 WAR for age related decline, so now we are down to 2.9 WAR. If you are willing to use a $4.5m/WAR conversion that get's us a salary of $13m.
Thome will definitely want a raise on his $1.5m salary in 2010, but I personally think that $13m is more than he is expecting or likely to be offered by any team. Maybe you think that his bat will decline more, or that he won't play 115 games (or that you caught an error in my math), so adjust accordingly.
I would be happy to pay him $10m to be our DH next year (if we can't have Cust for $4m). He would give us a 25-30hr threat who walks as much as Cust and, personally, he has always been one of my favorite non-A's. What do you think?