We toss our chicken in the sauce, then dress the pizza. If your sauce is spicy enough (as in, not mostly butter) you'll get the right flavor hit without needing all the drippy buttery messy sauce. Some pepper jack or even cheddar barely sprinkled over the pie helps hold the thing together.

Yes, it is sacrilege, but it is delicious.

Even though I think Buffalo wing sauce is a crime against all things pizza I wouldn't bother to "thicken" it at all. The real thing you need is a smoking hot oven; at least 500F. Use a ladle to spread the sauce over the dough. Depending on how well you've made your dough and how high your oven is calibrated it should be ready in about 5 minutes.

You could try to reduce it on the stovetop, but you'd have to contend with those mini-explosions that occur as the hot sauce starts frying in the butter. To get around it, pour the sauce onto a a non-stick baking sheet or into a shallow baking dish and put it into a 250-degree oven for a couple of hours to help dry it out. Or do what I do: buy a roasted chicken for $6 from the grocery store, pull off all the meat and rough chop it. Put it into a bowl and pour on enough buffalo sauce (Frank's and unsalted butter) to saturate the meat without it sitting in a puddle. The dough is topped with the sauced chicken and it gets baked. (If we are feeling sinful after a day of oatmeal and whole wheat, bacon and mozzarella will be sprinkled over the chicken.) When it's done, it gets a very light drizzle of Newman's Own bleu cheese dressing and a sprinkle of finely sliced celery. My four-doors-down neighbors thought this idea abhorrent until they tasted it, and now they make it almost every other week.

tomato puree?

For something like this cornstarch should work fine. But you will have to have enough to bring to a simmer for the cornstarch to thicken.

are you against adding tomato paste? Is it real wing sauce, as in butter and hot sauce? I suppose you could make a light roux with some of the butter and some flour, then add more butter and the hot sauce. Sort of like a spicy bechamel!?