The inlet hose (Bottom) on my 2005 Allroad 2.7T was hot, but the outlet one (top) was not. Same heat issue. Removed the battery to get full access to the hoses, unsnapped the thermal cover, worked them off the pipes and flushed the core with a garden hose and sprayer. No discolored crap came out. I used compressed air to blow the remaining water out from the top thru the bottom, reassembled and let the engine warm up - problem solved. I think my issue was excess air, as I had replaced the aux coolant pump in July 2012 and did not perform a full system flush and refill. Note, mix your G12 coolant with distilled water, not water from the tap.