The sketch that I posted is how your system should be set up to function correctly. Yes, your check valve is not where my diagram places it. Yours is all wrong. Someone messed with it in the past and had no idea how to reassemble it.
Right now you have a vacuum leak. Your car would prefer that you use that leaking air to control the cooling valve for the Tiptronic transmission. I believe that the default position for the valve it controls is to flow coolant and operating the valve stops coolant flow. Set it up as I pictured and it will function as designed. Plug the vacuum and the valve will remain in the default position. Leave it alone and your engine will run lean.
Here's a Buffalo, not far from where I live. She doesn't care what you do.
