@ Ian W...
Not sure I understand your comment.
Maybe I’m wrong (not as tech savvy as others on this forum) or was thought wrongly but this is the way I understand the different GPS/RNAV approaches…
As far as I know with the LPV approach you are not using a "barometric altimeter" to fly the assumed G/S like you would on a LNAV or LNAV/VNAV approach.
The LPV approach uses a GPS/WAAS derived altimetry to fly a very precise angular type G/S like an ILS and never changes regardless of the altimeter setting set on the altimeter nor does it change with the OAT, so there is no need to actually change the crossing altitudes over the various fixes on the approach like on a LNAV/VNAV approach to keep the proper ground clearance.
If you were to fly a LPV approach and you didn't set the proper altimeter setting (whether high or low) or if you did not "TEMP COMP" you would still be on that "proper and correct" G/S (like on an ILS) but your crossing altitudes over every fix on that approach would be either higher or lower than is written on the approach chart. You should still mentally do the “TEMP COMP” to have a correct idea of the “new” crossing altitudes over the fixes to double check but it does not need to be programmed in the FMS unlike a LNAV/VNAV approach.
Finally, you still need to readjust your DA (or MDA) to a higher minimum in the colder temperatures to keep that correct ground clearance.