The memory card is a big source of heat when writing but unlike a DSLR, if you are tracking the action through the camera then the sensor and display systems are always active even when you aren't capturing images and these generate significant heat in an enclosed space. If you are in a situation where you are using precapture, then the heat load is significantly higher. If you are used to shooting with a DSLR, the camera is nearly idle when it isn't actively capturing images with only the dedicated AF sensor (a very low power device compared to the image sensor) along with the dedicated processor for focus tracking are fully active thus little heat is generated.
With mirrorless, you need to be more careful of external heat sources (direct sunlight in particular) which greatly add to the heat load. The R1 is well sealed for use in bad weather which means its primary method of shedding heat is transfer via the camera body to outside air. If the sun is directly hitting the body, then instead of shedding heat it is adding even more heat. Mirrorless is just an evolution of the video camera and serious video cameras have long had active cooling systems, the downside is they aren't as forgiving of rain as a pro grade DSLR. Some lower levels of Canon cameras aren't as well weather sealed and they can more easily reject internal heat to the outside but the R1 is designed to shoot under conditions of moisture, dust, etc. that would damage a lower end body. The 1DX series used heat pipes to dump heat from the "electronics" area of the body to the fairly low temperature battery compartment but they have much less heat generation to deal with so the R1 is a different animal from prior 1 series Canon bodies.
There is NO perfect technology, every architecture has its tradeoffs and the methods you used in the past may require you to change to accommodate changing technology.
For me, the motivation to change from my 1DX III bodies to mirrorless isn't there yet because they do everything I need and without any special care. I have shot baseball in conditions where the camera bodies were hot enough that they were uncomfortable to touch but that was the only issue with them. For sports I always use at least a pair of bodies and lenses and although I am fairly careful to avoid having the camera not actively used not pointing into strong sunlight I would have to be far more careful with mirrorless architecture where the sensor would be what got zapped by excessive sun. I don't think a mirrorless sensor would like a few seconds of sun exposure from my 400 f2.8 glass while I am using the other body and lens to cover close in action.
So use your body to shield the camera when possible to keep it out of direct sun. It isn't like the mythical vampire that will turn to dust when sun hits it but the more it is in direct sun the faster its internal electronics will be forced into thermal protect mode.
Additionally most users buying R1 level cameras are willing to absorb the cost of expensive repairs if kept for a longer period of time but long before the camera goes into thermal protect mode it is developing a level of heat that is causing far more rapid aging of electronic components, especially electrolytic and tantalum capacitors. Thermal protection algorithms come into play to prevent immediate terminal damage to major components (the sensor, LNA and A/D converters, embedded control processors) but repeated operation resulting in high operating temperature degrades most electronic components. For those buying a mirrorless and wanting many years of near trouble free/service free ownership should avoid frequent operation under conditions where thermal warnings/protections are triggered.
Rodger
EOS 1DX M3, 1DX M2, 1DX, 5DS R, M6 Mark II, 1D M2, EOS 650 (film), many lenses, XF400 video
