Chris is correct in stating that as radiator caps age they often do not hold their rated pressure. I recently tested the cap that was on my car when I purchased it. Placing a section of heater hose in the heater water circuit along with a pressure regulator allowed me to use compressed air to pressurize the system. The cap held 4 psi. I installed a new 14 psi cap (which is proper for my '56) and retested it. The system now holds 12 psi. That's close enough for me.
The reason we run these cooling systems above atmospheric pressure is to delay phase change (changing from a liquid to a gas) as the coolant temperature rises above its standard atmosphere boiling point. The only way a lower pressure cap can cause overheating is if the engine gets hot enough to cause the coolant to change phase and blow of the remaining liquid coolant. Coolant, in its gaseous phase, is a very poor conductor of heat to say nothing of the fact that the water pump can't circulate it.
While it's true that in an adiabatic system when a gas is compressed it increases in temperature (as in Rudolf Diesel's remarkable invention), liquids are very resistant to pressure induced temperature change because they are, for the most part, incompressible.
Gary Kitterman
'56 C-73 "Babe"
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