t is my understanding that you can fly it within the temperature limit stated on the chart, BUT the DA or MDA should be corrected because it is not taken in account when constructing the path, in fact you can use different minima depending on the onboard equipment and certification, the path flown will be the same whatever minima you use, and will be flatter if cold or steeper if warm, but the minima should be temperature corrected.
Sorry, but that is not correct. Procedures are designed for the lowest common denominator, uncompensated. Depending on what you mean "correcting" you can get yourself in a lot of trouble.
Again...
When we design the procedure, there is the NA above and below temperatures. If you are between the NA above and NA below, the OCS has been validated to avoid the obstacles, from IF onwards.
In FAA land, the NA below takes you to a 2.75 degree glidepath (ICAO goes to a 2.5 GPA) The NA above takes to you a 3.5 GPA.
So uncompensated, you are between basically 2.5 and 3.5 degrees and the OCS has been validated for this.
Therefore, if you are within the temperature boundary, you do not need to correct the FAF nor the DA/MDA altitudes. Again, if the chart states uncompensated baro vnav, which I think they all do, or it is assumed uncomp.
IF you simply correct, while others are not, depending on when/what you correct, you run the risk of violating min separation.(or a host of other issues such as too high/too low)