2000 Nissan Quest, Hot air is coming out vents no matter what temp, setting is, And it gets warmer with engine temp. Vent selector works in all procession. Air condition is working so hard the hoses are sweating under the hood.

check for a broken /loose vacuum line on the engine . Trace it back to the fire wall and it will most likely be the culprit/

60degrees F is equal to 15.5 Degrees C . The temp of the air at the vent in the dash will be some where between 12 Degrees and 15 degrees C in a properly operating ac system and the thermostat in the cabin will control the air temp to around 18degrees C minimum. IT is important to understand that that what makes the air seem cold is the amount of water vapour in the air that is being taken out so allowing you to perspire more freely and not feel all hot and bothered. It helps if you set the dash control (Vent) to recirculate the cabin air and not allow outside air in

The blend door and blend door actuator control air temp, not the mode door. Mode door only controls WHERE the air comes out.

You will need to bleed the air out of the system there should be a bleeder where the top hose connects to the engine

I have seen this on GM vehicles before. If you take the temp selector and change it to the middle or to cool it will not let warm air go through the defrost vent. The hot air coming out of the defrost vent is because the heater core has warm coolant going through it- and the user generally has warm selected on the temperature setting.

iwould check the selector motor,and also replace the thermostant,start with the stant first,the selector motor is what runs the door for hot or cold the motor is a common problem,if the temp gauge is showing a quick warm up temp then its the selector motor, if it takes a while to reach operating temp then replace the t-stant,also make sure the coolant is full in radiator,check when cold or warm,dont open when hot, hope this is helpful.

sounds more like the thermostat may be failing. generally a water pump starts leaking out of the "weep" hole in the casting before it quits. just look at the front of the water pump for a greenish streak or an obvious leak.
if you also suspect you heater core may be getting plugged now would be a good time to back flush it to get rid of some of the gunk.

check the vacuum lines in the selector switch. the baffles that switch from hot air and cool air are vacuum controlled and if the lines are detached or cracked the suction will not move the baffles.

Damper/flap for driver's side is probably stuck. Try moving the selector from cold to hot several times. Also, move the recirc/outside air control if the previous doesn't work.

maybe...cuz the blend door may be not opening or closeing all the way