I have no hands-on experience shooting any of the R series cameras and my EOS 60D has only a mechanical shutter. So the OP's question seems a little confusing to me.
I tend to think of first curtain and second curtain sync, when used with a mechanical shutter, as only being of concern when shooting with a speedlight flash. It determines if the flash triggers shortly after the first curtain is fully open, or shortly before the second curtain begins to close. The function has no real effect when shooting only with constant ambient lighting. And I don't suspect it has any real impact on over-heating.
But it is my understanding that an electronic shutter, due to the scanning method it uses to record the image, also takes longer to process and load the image onto the memory card, which would produce some additional heat. And shooting at higher frame rates (fps) would magnify this issue.
It would seem to me that unless you absolutely need the higher shutter speeds and higher frame rates, and the silent operation offered by the electronic shutter, then using the mechanical shutter when possible would put much less heat stress on your camera. I'm curious to see what the experienced R-series shooters have to say about this.
