DSLR camera sensors are only exposed to light when the picture is taken, so the sensor presumably produces less noise than if it was always exposed to the light. I find support for this in the way Canon warns about Live View extended usage.
It's not the exposure to light that induces that Live View warning, it is the heat generated by the sensor being continuously energized. This heat is generated whether there is light falling on the sensor or not.
In the case of a camera being used in Live View, it's also exacerbated by the heat being produced by the camera's processor (almost always located closely behind the sensor inside most DSLRs and MILCs) that is providing 15-30 fps to the LCD screen on the back of the camera, the heat being produced by the always-on LCD screen, and the heat being produced by the battery providing energy to the sensor, the processor, and the screen.
This was particularly a problem a decade ago when DSLRs with Live View first started appearing. For instance, when some production companies first started using the Canon 5D Mark II for shooting television shows (most famously House), they had to swap out camera bodies after about 10 minutes of use due to the heat affecting the image quality.
As sensors have improved, it has been less of an issue. But a warmer sensor will always produce more read noise than the same sensor at a cooler temperature. That's why astrophotographers spend (tens of) thousands of dollars on actively cooled imaging sensors.
Canon tends to be very conservative with what they promise their customers about the capabilities of their products. In actual usage they often exceed those published performance parameters. Based on years of observations of the way Canon does business and the way they present their products to customers, my guess is that Canon still includes the warning lest any customer get upset that their camera is noisier when used with the sensor energized in Live View for several hours and then accuse Canon of not warning/informing them of the fact that image quality will be reduced as the sensor is heated.
There have been other camera companies that rush products to the marketplace without a vigorous testing program first. Some of them have had serious heat-related issues in the past due to small, compact cameras that couldn't passively shed heat as fast as they were generating heat.