Well, FWIW. I hate telling people this as they can take it as a recommendation but I'm at 117,000 miles on the same water pump and tstat. I KNOW the tsat has failed because the BT tells me every time I hook it up and the dealer told me when I took it in for the battery recall. It will be MUCH cheaper if I do it myself. Because its stuck in the open position I let it be and i dont want to go under there twice. Thats usually my luck, it would fail after a tstat change and id be under there again the next week. Now I have enough vehicles to not worry about a water pump failure downing the car. Not everyone's situation is similar. This car has been STELLAR so far unlike my X5 which I'm now wearing the hood shocks out by it being opened and closed so much.
My advice though would be to change both out at once as soon as you can. It's just me working on my cars with "little" help from the wife so I must manage time wisely as I do have fun and love the cost savings of doing all myself. The E60 is VERY reliable, and I'll argue that all day long. The E53 X5 however not so much. I'll argue that all day too.