Is the true altitude always lower than the indicated altitude as long as a correct local altimeter (QNH) is set on the altimeter? Given the fact that the altimeter setting is corrected for the temperature of the airport, on the condition that a correct local altimeter setting (QNH) has been made to the altimeter, is the true altitude always lower than the indicated altitude as the altitude increases above the airport elevation regardless of the temperature of the airport, since the temperature generally drops as the altitude goes up?
For example, even when the temperature in the airport is, say, above 30 degree Celsius, do we still fly lower than the indicated altitude of, say, 5000ft, just like when we do when the temperature is below 15 degree Celsius, standard ISA temperature?
No, the true altitude can also be higher than the indicated altitude, if the temperature is higher than expected from the International Standard Atmosphere (ISA). This case is usually not as important as the opposite case because flying at higher true altitude does not create a risk due to terrain clearance.

In a standard atmosphere, the indicated altitude
reflects the true altitude above the mean sea level
(MSL) and therefore provides a reliable indication of
terrain clearance.
Whenever, the temperature deviates significantly
from the standard temperature, the indicated altitude
correspondingly deviates from the true altitude, as
follows:

Extreme high temperature: the true altitude is higher than the indicated
altitude,
Extreme low temperature: the true altitude is lower than the indicated
altitude, thus creating a lower than anticipated
terrain separation and a potential obstacle clearance hazard.



(Airbus - Approach-and-Landing Briefing Note - 3.1 - Altimeter Setting - Use of Radio Altimeter)