OK, sounds like your thermostat is stuck, its a quick fix.
The hot coolant travels thru the DCCV to the heater so if the heater hoses are warm then the DCCV hoses must be warm.
There is a bleed valve next to the degas bottle, open it with a screw driver when the engine it hot, is the coolant hot? watch out! don't burn your fingers.
You can just loosen the screw to let the coolant drip out.
You might also need a new degas bottle cap, maybe its not holding the pressure.
When the DCCV goes bad the usual symptom is that you get one vent blowing hot air and the other blowing cold air. Check both passenger side and driver for a temp difference while running the A/C.
Just throwing some ideas at you.

My 01V6 is a major pain when it comes to heating and cooling. Mostly caused by cracking, leaking, air in system and Hydraulic fan failure. I was surprised to find the car will run and not overheat with the fan not working at all.