Let's discuss the heat theory.
First of all, the 1DX already shoots video at the same frame rates of the 1DC. The 1DX also does full resolution stills at roughly half the speed of that video. And as Canon's flagship stills camera it's unlikely they crippled the 1DX still image any with Nikon breathing down their back.
If Canon is doing additional things to cool the sensor for 4K video, to reduce noise and improve low-light performance, why wouldn't they do that also for the 1DX? I doubt it is sensor cooling.
The 1DX video does not line skip but instead reads the entire sensor at runs the result through a downsampling algorithm. Unlike the 5D3 it does not do pixel binning or any other shortcut. So the 1DX, sensor-wise is going to be the same in its operating heat as the 1DC.
The 1DC otoh doesn't downsample the sensor readout but instead crops it for 4K resolution. This is the computationally easiest operation resolution-wise, as easy as line-skipping was on the 5D2. Just discard information out of the frame.
It's conceivable that Canon improved rolling shutter performance for the 1DC over the 1DX by increasing readout speed. They haven't mentioned this, but if so, it will be very easy to test (mount both cameras on the same fluid head, pan back and forth and compare the distortion angles of vertical lines). Canon has the tech in-house as the rolling shutter performance of the C300 is excellent.
If that is not the case, then the only other matter is whether the DIGIC chips and CF cards will get significantly hotter processing 4K at 30fps than they do processing 18MP RAW+JPEG at 15fps (forgive and correct me if I don't have these specs memorized right). It's conceivable but I don't think it's so very likely.
They haven't added a fan to the body, they may have tweaked the heat sink approach a bit on the processor chips, but I have doubts that they could do much to improve a fundamentally passive design without visible modifications (such as metal fins or something).
So I call BS to the heat theory. Where is this additional heat coming from, and more importantly, where's it going?
It's just firmware dude. They may put something in there to make you think otherwise but there are so few of these being made at that price that I doubt it will be much.