Indeed, so outside temp could be factored into the tolerance and adjust accordingly, e.g: not triggering semi-false warnings when cold.
I’m not sure what you mean by false warning.
If the temperature is lower and the pressure is lower, you should inflate the tyre.
I don’t think you understand what the recommended pressure is.
When tyres are cold, they need a minimum pressure so that they don’t roll off the rim and the tyre contact patch gives safe driving in all conditions: rain or shine, town, motorway and anything in between.
That minimum pressure has to be met for safety reasons as it is impossible (right now) for the car to predict how fast you are going to drive and what kind of surfaces and if the temperature will rise or fall further.
It is indeed a ‘warning’. It isn’t a fault, it won’t stop you driving. If you know that the tyres will not be abused when cold, and they will warm up enough to get to 2.5 bar or above once at temperature, great. The warning will disappear.
It will come back when the pressure once again falls below the minimum.
For the record, in GT racing it is perfectly normal to drive a couple laps with the pressure warning on all tyres.
Dare I say many cars drive around with overinflated tyres, but I don’t think there’s a warning for that. Anything above 3 bar though I would be wary of.