I have had a few accounts of people telling that if you shoot (only a few hours of) video with Canon 7D / 5D Mark II, the quality of the pictures you take later becomes worse, due to the strain / heating put on the sensor.
Is that true ?
There are many reasons any given camera's images can become less sharp over time. I doubt you're going to get a solid confirmation, as it would be incredibly difficult to isolate this from other sources of sharpness reduction/variation, outside of perhaps a DxOMark laboratory (with controlled conditions, several brand new cameras, known-good lenses, etc).
Even if a few people agree, or even demonstrate with sharpness tests, there are many variations and other issues that can cause the same behaviour.
First up, any measure of sharpness will vary between single shots, anyone asking or answering this question should be aware that any testing/demonstration of this will require finding the sharpest images in a selection of shots taken in ideal conditions. Even changes in temperature/humidity might affect the sharpness if you're really getting picky.
Other sources of sharpness reduction
General use of the camera will mean bumps and knocks, of both camera and lenses. To test this properly, you'd basically need to keep the camera mounted on a tripod, with one single lens, in a controlled environment, and never move it.
Otherwise it seems likely that many cameras (especially Pro cameras that get a lot of use!) will take a few knocks and bumps along their life, and it's very easy to forget that time you put it down hard, or dropped your camera bag. Nothing noticeably broke/changed at the time, just like all the other times, but perhaps the AF sensor shifted slightly, perhaps the CMOS sensor shifted, perhaps a lens element shifted... and so on.
Other things can also do the same: environmental changes, cleaning of the camera, each shutter/aperture actuation, the list goes on...
In general, cameras deteriorate over time, for many reasons.
Humans as a source of data
Humans are very good at interpreting correlation as causation, and at making assumptions about how things work from very little data. This is both good and bad, in that it sometimes works well, and sometimes we get it very wrong. We also (unintentionally, and unconsciously) misremember things in a way that fits our understanding of the situation/system/laws of nature/whatever. We 'regenerate' memories based on our understanding, so if we believe that videoing caused our camera to lose sharpness, then we will remember events (perhaps incorrectly) in a way that supports this.
I won't offer my own opinion on the matter (for the 3rd reason) but would suggest this can only be definitively answered by some very controlled experiments (by trusted experts).