2002 Audi S4 Question Engine Stalling

I have a Audi S4 2002 with 127K miles. Over the past 2 or 3 year the car seems to stall within a short distance (with in 10 mins or so) from a cold start at home or after sitting for a few hours or will not start after a quick drive to the store. I have started to see patterns like more frequently on warmer days. Other observations include the coolant gauge gets to normal and the oil temp gauge gets to 200F about 25F from the normal and the car seems to stall at this point - at slower speeds or at intersections. At the Stall point only light that comes on it the battery like. I would then have to wait from 10 mins to over 60 mins before the engine will restart. My observation at this point are that the oil gauge temp has cooled down to about 150F or so and the coolant gauge is still at normal or just move off the normal setting. This will happen once a day this after that all is fine till the next dayâ� ¦
Are the any sensor or relays that protect the engine from overheating maybeâ� ¦or other things I can look into.