The "nowhere" end of the capillary tube should be located in the output air stream. In theory, it is supposed to sense the output air temperature and operate a valve which automatically adjusts the water flow through the heater core. In practice, well, you can see what happens when these controls get old. Consider yourself lucky that the problem isn't worse. These valves will often develop an external leak.
If you are doing a stock resto for points, there are outfits which can rebuild these controls. Here is a link to one (Disclaimer: I have never done business with this company), and a Google search will turn up more of them.
http://www.heatercontrolvalve.com/
If all you want to do is drive the car without roasting, the simplest fix is to install a manual valve in one of the hoses (either hose - it doesn't matter which). You can also get a cable-operated valve which can be connected to your stock heat control on the dash.
Ray
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