Altimeter error (non-standard air)

The altimeter always assumes the standard atmosphere (15 °C, 29.92", cooling 1.98 °C/1000 ft). When the real air differs, the indicated altitude is wrong even with the correct setting.

Three-pointer sensitive altimeter face — The three-pointer sensitive altimeter. It reads pressure against the standard atmosphere, so non-standard air makes the indicated altitude wrong. Bsayusd, via Wikimedia Commons (public domain).

Pressure: fly toward lower pressure (or hold an old, too-high setting) and the altimeter over-reads, so your true altitude is below the indication (TC AIM AIR 1.5.3).
Temperature: air colder than ISA is denser, the pressure levels sit lower, and again you are below the indication (TC AIM AIR 1.5.4). Warmer than ISA, you are above it.

Trap: "From high to low (pressure or temperature), look out below." The altimeter reads high, so you are lower than it shows.

References

TC AIM AIR 1.5.3
TC AIM AIR 1.5.4

PPL Tester

Altimeter error (non-standard air)

References

Practice