What kind of car? Is it an AC car?
When you say it runs all the time, do you mean the fan is blowing? If so, then either the switch is bad or the resistor down on the box is bad (although a bad resistor usually means the opposite, no fan at all).
Generally the only control you have is the fan speed and the internal vent (which either lets hot air blow in or not). If your fan is running all the time then yes you will have heat all the time. The fact that you are regulating it via the temp knob means that you are opening or closing the internal vent/door to regulate the amount of hot air being fed into the cabin of the car.
If you don't want/need heat then you can either disconnect the fan switch (at the heater or at the switch) or even pull the fuse. If you want it to work correctly, then you need to determine what the actual problem is, I suspect it is the heater switch itself as they are prone to failure after many years.
You can many times fix these switches, there are little arms that hold the rear of the switch on which have to be pried up very carefully (you do not want to break them). Be sure to keep a firm grasp on the back of the switch as you pry up the little arms because there is a spring in there). Once you get the arms up, very carefully take the back off and look in side. They are very simple switches and after a minute or two of looking at it you will see how it works. Carefully take everything out, clean all of the contacts (degrease, use a little sand paper), then reassemble using some dielectric grease which will provide lubrication and resist future corrosion. If you do it right and the switch isn't seriously damaged it should work like new.