It is somehow true! For a moment, forget about the live view and consider the case of long exposure. While long exposing, the sensor heats up and this will cause the infamous background noise. So in reality sensor over heating can cause the noise and what happens is that in low light, warmed pixels detect light when there is none. (This last sentence is very not-scientific but naïvely explains the problem!)

This being said, you should consider that in day-light shooting this noise is almost completely harmless because the input signal is strong. But in low light condition this noise can be noticeable. How much noticeable? It really depends on the camera! One of the links below, shows some photos for comparison:

They also state that:

The camera warms considerably in Live View, more so than during the 60 minute exposure but this might simply be due to the LCD screen itself rather than due to the sensor being active.

Which means, the resulting noise is also highly relate to design of the camera body. For further readings, please refer to the links bellow.

Using live view for landscape photography

Long exposures and sensor noise with Canon 5D2