Rated power vs. temperature for resistors
Pulses are a whole separate section of the datasheet. If you have high power pulses at far above the DC limit but low repetition frequency, you cannot use average power. If the datasheet does not have a pulse section, then you should stay under the DC limit (or find another resistor).
For example, if you have a pulse which is 10x the rated power, but occurs infrequently, that pulse may still blow the resistor even if the average power calculation is below the limit in your curve.
For non-pulse waveforms that have a high repetition frequency, you can use the average power calculation. RMS power is not really what you want. You want to average the power over one full period of the waveform.
Here is a snapshot of a pulse repetition section from a pulse rated resistor.
(http://www.vishay.com/docs/20044/_crcw37.pdf)

Once you get to 100 seconds you are basically at the DC limit. But for 1us the resistor can dissipate 10,000x the DC limit.
Not all resistors are not going to be like that.