And Max has highlighted a second real problem. If the ATC procedures have already taken account of the temperature but the pilot also applies a correction, the separation between aircraft will be eroded. Taking the extreme example of -40 that is given, the nominal 1000ft vertical separation from the next higher allocated level will, in fact, be just 30ft.
Northbeach's original question and glf's input therefore become pertinent - it's important for the pilot to know who has responsibility for applying the correction. Another hunt through the books suggests that it's not clear.
I presume that when faced with this question in an operational situation, pilots will ask ATC whether temperature corrections have been incorporated in the procedures being used. What sort of answers do you get?