Wow. Trust me, you are not alone in wondering what the heck the title of this post means. I don't usually do this on Productive Catholic, but @HumanaeVitae suggested that I try this post last night when I got writer's block and couldn't think of a good post. The question of impassibility is in various places of St. Thomas Aquinas' Summa Theologica, but as my friend pointed out Question 82 of the supplement to the Summa is where the meat is. Rather than writing a whole treatise on the concept (since that has already been done by St. Thomas) I though that I'd make a short video that detailed my thoughts on the subject. In short, you will see that the problem of impassibility is nothing a little alcohol can't fix.
If you want a more in depth explanation of the impassibility of the resurrected body, you can check this out!