nnc0,
If the crossing altitude/height is corrected for temperature, the angle should be the desired original angle and subsequently the FPA would not require any correction, assuming that you are flying the Flight Path Angle.
In practical terms the glidepath generated from the ground will not change and for example the altitude corrections on an ILS is to enable FAF altitude cross check and Minimums correction to prevent descending below the desired decision height.
If the approach is a non-precision type, the calculated FPA will still remain the same, if in fact you are flying a specific descent or glidepath angle, and the corrections to the altitude are to provide proper heights at procedure altitudes and fixes, (ie procedure turn/inbound prior to FAF, FAF crossing altitudes, MDA, MSAs etc.) as well, the vertical speed, if sourced from a barometric source will also reflect the changes.
The geometry remains the same, the indication on the barometric altimeter/VSI are merely reflecting the errors due to the cold air mass and are subsequently corrected to ensure the geometry remains the same (and the obstacles are cleared).
BD