ok your heat comes from the heater core, as im sure you know, if you take of the top cover of your a/c box you'll see the heater core and a door that's mechanicaly operated by the lever in your car, you slide it towards heat and the door opens into the box air stream, when you close it it isolates the heater core so you would only get cold or ambient air temp blowing. Also that purple line is for your vent controls you should have an off white one to. but im gussing that your door isn't operational or stuck half way open, keep in mind with no a/c it will blow hot air if its hot outside...90 degrees outside your blowing atleast 85 degrees inside
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