rrtxdrvr

Totally puzzled here in Texas. I have no heat in my 06 xA. I pulled out the thermostat, flushed system with product, drained refilled with water. No heat. Drained and back flushed the heater core, (no clogs) refilled with water, still no heat. I noticed the right hose to the heater core is only warm while the left one is cold even after idling for about 20 minutes. I understand there is no heater valve but don't understand why the coolant doesn't seem to be circulating from the engine and through the heat core to produce heat inside car. Blower is fine, just cold air. Any ideas on this is greatly appreciated.
Stumped in Texas