The dual climate system uses just one heater core. However, there's a divider inside the heater box, and two "air mix" vanes, one for each side. The two vanes direct air through or around the heater core depending on the temperature setting.
It's possible that the heater core is somewhat clogged on one side, so that even with the vane set to direct all the air through the core, there's little warming of the air. Another possibility, which is not uncommon, is that the actuator (electric motor) that adjusts the air mix vane for the passenger side isn't working, and is stuck at the cold setting.