2005 Suzuki Forenza heat

Is the engine warming up to normal temp? With the engine running, warm, and the heater on high, do both heater core hoses get hot?

It sounds like the heater core is plugged. Remove both radiator hoses and spray water through it to see if the water will flow through.

Let me know what happens.

NOTE: You will lose coolant when you remove them. Make sure the engine is cool and you have something under the vehicle to catch the coolant that is lost. I often times will put locking pliers on both hoses to squeeze them shut and prevent much loss.