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Well, derating is more of specifying a maximum power setting at less than max rated power to prolong its life, e.g., piston engines in a helicopter. This has the added benefit of being able to sustain max power higher up. Like if BMW derated the S65 to 300 horses. Obvi, you would be able to maintain that HP over a lot of altitudes and temps.
Your examples are more along the lines of not being able to use rated power because of another factor, such as temp limits. That certainly has the effect of derating it for that moment in time but it's not the normal usage of the term, derating applying beyond specific situations.
The bottom line is, all other things being equal, hot air is less dense (much like having a car at altitude). Less dense air makes less power.
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