Help!

My heater on my 2010 RDX (base) blows but doesn't heat. One of the hoses that take coolant through the firewall to the core gets warm/almost hot. The other hose stays cold even when the engine is at running temperature. Can I conclude that the core is clogged? Is there a valve somewhere that controls coolant going to the core?

I'm trying to flush the core. Water does not enter the exit (return hose).

The A/C works well.

 

Based on what I see in the diagram, there aren't any valves between the firewall and core. Not changing the coolant at recommended interval can cause the core to plug.
https://www.acuraoemparts.com/v-2010...l--heater-unit

 

Acura RDX 5 Door TECH KA 5AT Heater Unit - There is a drain hose click here to see parts lists and diagrams...I would drain it then flush with water and then fill it with oem coolant.