I have a 2006 Hyundai Tucson v6 and the heat stopped working. It blows out fine but only cold air. I've checked the coolant level which is fine and all fuses that relate to the heat and ac.
In your vehicle there is a heater core inside the dashboard. Engine coolant runs through this core all the time. There is a small door inside the HVAC (Heater, Ventilation, Air Conditioning) system that controls air flow through the heater core. When you want full cool that door shuts off all airflow through the core. In full heat mode all the air is forced through the core. That door is controlled by either a cam and cable or by small electric motor and plastic gear train.
I'm pretty sure you have the electric motor version. If none of the different HVAC modes work check your fuses. If everything works but the heater blend system you've probably got a bad motor control element (or perhaps broken plastic gear in that doors drivetrain.)
I'm guessing that if you try to adjust the temperature on the controls (key on, engine OFF, radio OFF, low blower), you will hear some odd clicking sounds from inside the center of the dash board.