Gotta ask, why does that cause the coolant level to rise in the expansion bottle?
Coolant expands when it gets hot, but not enough to fill the expansion tank and overflow!
However temperature of the coolant is the reason the coolant overflows when the cap fails to hold pressure!
Water at atmospheric pressure boils at 100 degC
Water at 1 bar above atmospheric pressure (cooling system pressure) will boil at about 125 deg C
When water heats up it first gently releases dissolved gasses (nitrogen and oxygen), which causes the pressure rise in the coolant system. In a closed system, such as the F/TF cooling system, this building up of pressure provides equilibrium to prevent the coolant boiling. (In a sealed pressure vessel water will never boil!!!).
So long as the temperature of the water does not exceed the boiling point, for its pressure, then the coolant system stays in equilibrium and will not boil.
The F/TF cooling system keeps the coolant temperature at about 110degC and a maximum pressure of 1Bar over atmosphere, so as long as the system is pressurised to 1bar, and the temperature does not exceed 125degC it will not boil
However if the pressure is reduced to atmospheric, with a leaking cap for instance, its boiling point will be reduced from 125degC to 100degC but the actual coolant temperature is still about 110degC.
As the water now starts to boil it now rapidly releases large quantities of water vapor (steam) which is a lot less dense than water so expands in volume. This forms large bubbles in the coolant (like when a kettle boils) which displace the coolant out of the expansion bottle, casing it to overflow.
So excess temperature
at reduced pressure
, cause the water to boil, which displaces the water out of the expansion bottle.
You did ask