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No, they don't need cooling. They do get warm, and the case gets warm, but so far it's well below the temperature at which the PLA would deform. I just did an hour-long print and the lid was warmest above the TL-Smoother for the extruder, and it felt like it was maybe 30 or 40 degrees. (Warm, but not hot to the touch, and definitely below 60 degrees.) The temperature also seemed to remain consistent throughout the print, so I believe it won't get any hotter than that on longer prints.
Lastly, I have fairly high-torque motors that require a high amount of current (2.4 A max), so I expect my thermal conditions to be near the high side of the range. Your thermals will be different based on your stepper drivers and how much current they're putting out, but I expect the case will work OK for most people.
I'd definitely invite a remix of the lid that adds a grill just to get some airflow though. Just make sure the grill spacing is small enough so that dropping a screwdriver or screw on it won't go through and short it. That's my pet peeve with case designs on Thingiverse. :)