Take off performance may be the least of the issues of operating in high ambient temps
You are quiet right, and most of the FAR 23 manuals I've looked at have the following statement in the performance section,
Satisfactory engine cooling has been demonstrated for this airplane with an outside air temperature 23°C (41°F) above standard. This is not to be considered as an operating limitation. Reference should be made to Section 2 for engine operating limitations.