With regard to cooling....depends.
Some motors are less efficient than others (can you say hobbyking).
I spent a BUNCH of time looking over every single suitable outrunner for my Funjet and finally rejected them all.
Cheap, yes, but they make more heat for the same output.
OTOH and ES isn't a Funjet.
Some inrunners have cooling holes...others do not.
So....there are LOTS of variables in addition to the basic question.
If you run a given prop
on 2S the power it will pull will be a lot less than 3S > so, heat output will be lower.
OTOH, if you are flying around at 1/4-1/2 throttle all the time it may not matter much.
As indicated, you don't PUSH power. Power is determined by the load on the motor which is a function of the prop and voltage. Since you really can't change the prop much in this instance, your biggest variable is the voltage.
In applications where the prop is not a limitation you can prop up or down to make a 2S (larger prop) and a 3S (smaller prop) pull approximately the same. The 2S will pull more AMPS as the voltage is lower-simple electronic math. That's why if you are PUSHING the motor envelope higher voltage and smaller props are more desirable, within limits.
You can go for inrunners with different KV. A stock Stryker C is around 1900kv and is happy on 3S with that prop size.
Something like the eFlite Six-Series Brushless 2700Kv Motor
would be loafing on 2S and screaming on 3S.