Basically you have the blower motor that draws in outside air (or recircs cabin air) and blows it through the ducting in the dashboard. Inside the dash is the heater core (hot) and the AC evaporator (cold), and a blend door that directs air from the blower through one or both of them as you move the temperature slider back and forth. So if you want cold air, the blend door directs air through the AC evaporator, if you want hot air the blend door directs air through the heater core. If the blend door stops working (broken cable or actuator or whatever) then you lose control over hot/cold.
You have heat in the core? Check the hoses, if the return hose is hot then coolant is flowing through the heater core so its not obstructed.
You have air from the blower? If you feel good volume then that is working
Probably the blend door