Yes your screen shows the timer, but that is not live-view.
Besides, the timer screen is on in bulb mode whether you use live-view or not.
The sensor gets hot in live-view because it is in video mode and is constantly being read from, this means all the amplifiers and shift registers and other electronics are powered up continuously.
A timed exposure is different, the amplifiers and most other electronics on the sensor are turned off, the sensor uses very little power while being exposed, until you tell it to stop the exposure and everything powers up to read out the pixels and amplify/convert the signals etc.
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