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If it is an original radiator, then NO. The older style radiators, with large volume reservoirs at the top and bottom, are simply not strong enough to handle the higher pressure. From basic physics -- the wall stress of a chamber goes up as a square of the diameter of the chamber -- this means that given equal pressures, a large volume reservoir on the radiator is much more likely to blow up like a shook-up can of Coke, as compared to a small volume reservoir.
Now, I have heard that replacement radiators these days are made enough stronger that they will handle the 13lb caps. But, the cooling gains are marginal, and if you are not getting things cool with a 7 lb cap, then you are probably not going to solve things with a 13 either. And the resultant leak or ballooned radiator you may possibly get is not going to cool very good either.
Well I have determined the radiator was replaced in the late 70's. So this is probably the proper cap for it. I still don't understand why I am constantly losing coolant.
Have the cap checked to see if it's holding pressure at 13lbs. It may be failing and blowing cool.ant out the overflow. Any radiator shop or a good mechanic will have a device to test it.
Yesterday I was working on #&%* Voltage Regulator so I did actually watch it work with the new radiator cap (13Lbs). Engine gets hot, reservoir level goes up, Engine cools down, reservoir level goes down. I didn't see any coolant loss at all. Maybe the new cap fixed the problem. I'll wait and see, especially on a hot day...