So what have we established? In extreme temperatures, either low or high, there can (and most likely will) be a discrepancy or deviation or difference between the real altitude and the altitude shown on the altimeter, even if set to the correct QNH.
Q1: how to determine said discrepancy?
A simple rule of thumb is that the error is 4ft per 1000ft above the airfield for every degree C deviation from ISA.
For deviations that are colder than ISA, subtract the correction from the indicated altitude.
For deviations that are warmer than ISA, add the correction to the indicated altitude.
From this, you can see that with a cold deviation, the altimeter will over-read, in other words, you will be lower than you think you are.
As a deviation in the cold sense is more dangerous, let's discuss that first.
The deviation from ISA, technically speaking, is the average temperature deviation of the airmass between the altimeter and the QNH reference. In other words, it is a measurement of how cold the air is below the aircraft. (The colder it is, the more 'compacted' the isobars will be in a vertical sense.) In most cases that can be translated more simply as taking the airfield OAT and calculating how this differs from ISA.
Example 1:
Airfield elevation 500ft
Airfield OAT 14C
QNH 1000hPa
ISA temp Dev 0
Altimeter set to 1000hPa
Indicated altitude 3500ft (3000ft above the airfield)
Calculated altimeter error is 4x0=0ft per 1000ft
True altitude 3500-0=3500ft
Example 2:
Same as example 1 except
Airfield OAT 4C
ISA temp Dev -10
Altimeter set to 1000hPa
Indicated altitude 3500ft
Calculated altimeter error is 4x10=40ft per 1000ft
True altitude 3500-(40x3)=3380ft
So, although you are actually just over 100ft lower than you think you are, this is not a huge problem and note that the error will reduce as you descend closer to the airfield, eventually reaching zero as you touch down. This is why altimeter temperature error is not considered important for most PPL VFR flight operations and hence most PPL holders have not heard of it.
For IFR operations, the error can be operationally significant. As the error increases with altitude, high ground close the airfield can be problematic when calculating MSA and minimum holding and procedural altitudes that are significantly higher than airfield elevation.
Example 3:
Airfield elevation 500ft
Airfield OAT -6C
QNH 1000hPa
ISA temp Dev -20
MSA 8700ft
MHA 9000ft
Altimeter set to 1000hPa
Indicated altitude 9000ft
Calculated altimeter error is 4x20=80ft per 1000ft
True altitude 9000-(80x8.5)=8320ft
So now you are nearly 700ft lower than you think. In fact, you are 400ft below the MSA. If you are in IMC, that is not a good place to be!
Again, in this example, the error would reduce as you descend, reaching zero as you land.
What can you do about it?
A/ Be aware that this is a real feature of all barometric altimeters.
B/ Be especially careful when the airfield OAT is significantly (e.g. 20 degrees C) colder than ISA.
C/ Remember that the error increases with altitude, so be more careful in areas where the MSA is much (e.g. 4000ft) higher than the airfield elevation.
D/ Ask ATC for a higher level/altitude. ATC may have issued their clearance having already allowed for cold temperature corrections.
What you must not do is arbitrarily fly at a higher altitude than that given by your ATC clearance. That could reduce vertical separation from other traffic.
If you are not happy with the cleared altitude, ask for a higher one, explaining your concerns if required. A simple statement like, "my operational minima require me to maintain _____ft" can work wonders.
For deviations that are warmer than ISA, the same arithmetic applies but the final correction is added to the indicated altitude. This has the effect of increasing your terrain clearance and therefore is not seen as a safety issue.
Warm deviations can cause confusion nevertheless.
Consider the following:
Airport elevation 500ft
QNH 1000hPa
Airport OAT 34C
ISA temp Dev +20
ILS glide slope intercept at 12nm and 4400ft
Altimeter set to 1000hPa
Indicated altitude 4400ft
Calculated altimeter error is 4x20=80ft per 1000ft
True altitude is 4400+(80x3.9)=4712ft
You are now just over 300ft higher than you think you are and will intercept the ILS glide slope at 13nm, instead of 12nm.
How relevant is all of this in the real world?
Cold
I have renegotiated higher holding altitudes at Innsbruck.
I have flown higher altitudes on a DME arc at Iqaluit.
Warm
I have had some issues with glide slope intercept at Mauritius and Mexico.
I have adjusted my altitude whilst flying aerial surveys in Saudi Arabia.