In long periods of recording video, yes, in my experience (NEX 5, NEX 5N) you'll eventually push them into heat shutdown. For still use, I've not triggered a heat shutdown, though I believe it to be possible (perhaps in extremely hot weather with very frequent shooting). With "regular" shooting, I don't deem this to be a huge issue worth worrying about. However, do note that heat causes electron migration within a sensor and thus increases noise tendencies.
The newer A#### models seem to be better at heat dissipation than the old NEX models. But I’ve still managed to push an A6000 into heat shutdown.
The A7 models seem even better at heat dissipation, but be aware that they, too, will shut down if heat goes beyond a trigger point.
Simply: try not to use these cameras for long, uninterrupted periods of video, and keep them out of direct sunlight as best you can when you do.