You'll have higher oil pressure on start up with a cold engine at idle because the oil is thicker. As it warms up, oil pressure will drop down at idle because the oil is thinner.
In both cases, when it reaches a certain value (a bit over 3 bars), it will not get ant higher (cold or hot)
Basically, all parts of the engine (including head gasket) will never be subject to a higher oil pressure than what has been designed by the engine builder.
If you have leaks, I would completely forget about high oil pressure (hot or cold) as being the reason or cause for the leak.
There is a defective gasket or oil seal somewhere. Do not look further.