As you suspect, it does need to cool as heat will build. From another thread where I had corresponded with Lucien who helped develop the Cobra from Pulso,
"Lucien at Innov8tive responded to my temperature question - "When I do the testing on the motor, I do not like to see the core of the motor exceed 160˚ F. That is the point where I call the “Max Current Point” on the Cobra motors during my prop tests. The “Can Temperature” will typically be about 30˚ F cooler than the core temperature." and "The magnets used in the motors are rated for 150˚ C (302˚ F) but you really never want to get them that hot. Likewise, the insulation on the winding wire is rated for the same temperature, but you can get localized heating on the inside strands of the wire, closest to the stator core, that can be significantly hotter than the core itself." "If a motor is getting that hot, then you either do not have enough cooling, or you are simply pushing the motor too hard for the application."
The time to cool will depend on air temperature and movement as you are sitting trying to cool. Leaving the battery cover off can help, and some have developed a small battery fan to speed up cooling, but you are stuck waiting. Then use an IR thermometer and shoot the motor. I try to shoot the nonmoving portion if able as it is the hottest. You can fairly quickly develop an estimate of how long to wait considering ambient temperature and the measurements. Hope that helps.