For the rear Heat/AC system the hot air is supposed to come out through the floor vent (right next to feet if sitting in middle bench, driver side), and the AC or vent (cold) air is supposed to come out through the wall and roof vents.
Easy check, When the engine is cold, check your coolant level, this sounds to me like a classic, low coolant thing. If you haven't changed your coolant in a while, I'd suggest changing it. If you never changed it since new, you may have clogs in the radiator and heater core, due to the OEM coolant had a high silica content, which made sand-like clumps if left in the car too long. I had to blast air through my overflow tank line to clear the sand clumps from it. (The rest of my cooling system is brand new

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1998 Ford Windstar GL 3.8L 252,300 miles
2005 Toyota Prius Package 6 1.5L 133,000 miles
2006 Toyota Sienna LE 3.3L 34,000 miles
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