The minimum temperature secified on the chart simply ensures that the VPA which of course changes with temperature does not get too low.
Pilots still must make the appropriate temperature corrections for the various promulgated altitudes/heights in the normal way.
To explain further:
If the VPA is 3deg at 15C
It will be only 2.5deg at -31C
So as the temperature decreases the VPA gets more shallow and the minimum temperature limits how shallow the VPA can get.
Imagine an ILS GP that changed from 3deg at 15C to only 2.5deg at -31C
With a lowering VPA then the obstacle surface must also lower and there will be a limit on how low the obctacle limitation surface can go.
The movement of the VPA does not remove the requirement to ensure that the actual level of the aircraft at for example the DA(H) (indicated level corrected for temperature) is not below the true level of the DA(H).
Hope that explains the two different requirements.
Regards,
DFC